This MCQ module is based on: 5.1 Common Multiples and Common Factors
TOPIC 16 OF 41
5.1 Common Multiples and Common Factors
🎓 Class 6
Mathematics
CBSE
Theory
Ch 5 — Prime Time
⏱ ~16 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: 5.1 Common Multiples and Common Factors
Targeting Class 6 level in Number Theory, with Basic difficulty.
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5.1 Common Multiples and Common Factors
This chapter, titled "Prime Time", explores how numbers relate to one another through multiples?, factors?, and the special class of numbers called primes?. We begin with a lively classroom game.
The Idli-Vada Game
Imagine a group of children sitting in a circle. They count aloud one by one: 1, 2, 3, 4, and so on. But there's a twist — whenever a player's number is a multiple of 3, they say "idli" instead of the number. When it is a multiple of 5, they say "vada". And when the number is a multiple of BOTH 3 and 5, they say "idli-vada"!
Those numbers — like 15, 30, 45 — which appear in the multiples of 3 AND in the multiples of 5 — are called the common multiples of 3 and 5.
Key Idea
A number \(n\) is a multiple of \(k\) if \(k\) divides \(n\) without any remainder. A number that is a multiple of two (or more) numbers at the same time is called their common multiple.
Fig 5.1 — Venn diagram showing multiples of 3, multiples of 5, and their overlap (common multiples).
🔵 Try: At what number would the player say "idli-vada" for the 10th time? Since common multiples of 3 and 5 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 — the 10th "idli-vada" is at 150.
🔵 If the game is played with the numbers 1 to 90, how many times will the children say "idli-vada"? Common multiples of 3 and 5 up to 90: 15, 30, 45, 60, 75, 90 — that's 6 times.
Playing with Different Pairs of Numbers
Let us try the Idli-Vada game with other pairs. For each pair, the numbers where BOTH conditions are met — where the player says "idli-vada" — are the common multiples.
For which pair(s) below, and up to 60, find all the common multiples (first three):
(a) 2 and 5 (b) 3 and 7 (c) 4 and 6
(a) 2 and 5 (b) 3 and 7 (c) 4 and 6
(a) Common multiples of 2 and 5: 10, 20, 30, 40, 50, 60.
(b) Common multiples of 3 and 7: 21, 42, 63 (only 21 and 42 are ≤ 60).
(c) Common multiples of 4 and 6: 12, 24, 36, 48, 60.
(b) Common multiples of 3 and 7: 21, 42, 63 (only 21 and 42 are ≤ 60).
(c) Common multiples of 4 and 6: 12, 24, 36, 48, 60.
Jump Jackpot — Multiples on a Number Line
Jumpy and Grumpy invent a game. Jumpy places a treasure somewhere on the number line, starting from 0. Jumpy makes jumps of the same size — say, jumps of 4. If he lands on the treasure, he wins. Can he reach 24 using jumps of size 4?
\(0 \to 4 \to 8 \to 12 \to 16 \to 20 \to 24\) — yes! 24 is a multiple of 4. Other sizes that work: 2, 3, 6, 8, 12, 24 (each divides 24 evenly).
Jumpy reaches the treasure at 24 using jumps of size 4.
Factor / Divisor
Each of 1, 2, 3, 4, 6, 8, 12, 24 divides 24 evenly — these are the factors (or divisors) of 24.
Common Factors
Numbers where two players (Guna jumping by size \(m\) and Grumpy jumping by size \(n\)) BOTH land together are common multiples of \(m\) and \(n\). Numbers that divide both of two given numbers are the common factors of those numbers.
🔵 What jump size can reach both 15 and 30? Any common factor of 15 and 30: 1, 3, 5, 15.
Factor tiles — any number in red is a common factor (a valid jump size that reaches both 15 and 30).
Perfect Numbers
The number 28 is special: the sum of its factors excluding itself is 1 + 2 + 4 + 7 + 14 = 28. A number with this unusual property — sum of factors (other than itself) equals the number — is called a perfect number. The next perfect number after 28 is 496.
Figure it Out (Section 5.1)
Q1. Find all multiples of 40 that lie between 310 and 390.
Multiples of 40 in this range: 320, 360.
Q2. Who am I?
(a) I am a number less than 40. One of my factors is 7. Sum of my digits is 8.
(b) I am a number less than 100. Two of my factors are 3 and 5. One of my digits is one more than the other.
(a) I am a number less than 40. One of my factors is 7. Sum of my digits is 8.
(b) I am a number less than 100. Two of my factors are 3 and 5. One of my digits is one more than the other.
(a) Multiples of 7 under 40: 7, 14, 21, 28, 35. Digit sum 8 → 35.
(b) Multiples of 15 under 100: 15, 30, 45, 60, 75, 90. Digits differ by 1 → 45 (4 and 5) or 45.
(b) Multiples of 15 under 100: 15, 30, 45, 60, 75, 90. Digits differ by 1 → 45 (4 and 5) or 45.
Q3. A number for which the sum of all its factors is equal to twice the number is called a perfect number. Show that 28 is a perfect number.
Factors of 28: 1, 2, 4, 7, 14, 28. Sum = 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28. Hence, 28 is a perfect number. (6 is also perfect: 1 + 2 + 3 + 6 = 12 = 2 × 6.)
Q4. Find the common factors of: (a) 20 and 28; (b) 35 and 50; (c) 4, 8 and 12; (d) 5, 15 and 25.
(a) 1, 2, 4. (b) 1, 5. (c) 1, 2, 4. (d) 1, 5.
Q5. Find any three numbers that are multiples of 25 but not multiples of 50.
Multiples of 25: 25, 50, 75, 100, 125, 150, 175. Remove multiples of 50 → 25, 75, 125.
Q6. Anshu and his friends play the idli-vada game with numbers 14 and 10. Which of these players gets to say 'idli-vada' after 50 but before 80?
Common multiples of 14 and 10 are multiples of 70 → 70.
Q7. In the treasure-hunt game, Guna has kept treasures on 28 and 70. What jump sizes will land on both the numbers?
Common factors of 28 and 70: 1, 2, 7, 14. Jump sizes: 1, 2, 7, 14.
Q8. Multiples of 3 and multiples of 4 — fill in the empty Venn regions.
Multiples of 3 only (up to ~50): 3, 6, 9, 15, 18, 21, 27, 30, 33, 39, 42, 45. Multiples of 4 only: 4, 8, 16, 20, 28, 32, 40, 44. Common (multiples of 12): 12, 24, 36, 48.
Q9. Find the smallest number that is a multiple of all the numbers from 1 to 10, except for 7.
LCM(1,2,3,4,5,6,8,9,10) = \(2^3 \cdot 3^2 \cdot 5 = 8 \cdot 9 \cdot 5 = 360\). 360.
Q10. Find the smallest number that is a multiple of all the numbers from 1 to 10.
LCM(1..10) = \(2^3 \cdot 3^2 \cdot 5 \cdot 7 = 8 \cdot 9 \cdot 5 \cdot 7 = 2520\). 2520.
Activity: Play the Idli-Vada Circle Game
L3 Apply
Materials: A group of 6–10 friends, chalk circle, notebook
Predict: How many times will "idli-vada" be said if you play with multiples of 4 and 6 from 1 to 100?
- Sit in a circle. Pick two numbers, say 4 and 6.
- Count from 1 onwards. Say "idli" on multiples of 4, "vada" on multiples of 6, and "idli-vada" on common multiples.
- Keep a tally of each on the blackboard.
- At the end, list every "idli-vada" number and verify: these are the common multiples of 4 and 6.
Common multiples of 4 and 6 = multiples of 12. Up to 100: 12, 24, 36, 48, 60, 72, 84, 96 → 8 "idli-vadas".
Competency-Based Questions
Scenario: Two signal lights on a highway flash independently. The red light flashes every 12 seconds and the green light flashes every 18 seconds. Both are switched on together at 6:00:00 AM.
Q1. After how many seconds will both lights flash together again for the first time?
L3 ApplyNeed the smallest common multiple of 12 and 18. Multiples of 12: 12, 24, 36, 48… Multiples of 18: 18, 36, 54… Common = 36 seconds.
Q2. How many times will both lights flash together in the first 5 minutes?
L4 Analyse5 minutes = 300 s. Simultaneous flashes at 0, 36, 72, 108, 144, 180, 216, 252, 288 s → 9 times (including the start).
Q3. A third light flashes every 30 s, also starting at 6:00:00 AM. Evaluate: when will all THREE lights flash together for the first time?
L5 EvaluateLCM(12, 18, 30). 12 = 2²·3, 18 = 2·3², 30 = 2·3·5. LCM = 2²·3²·5 = 180 s = 3 minutes. First joint flash at 6:03:00 AM.
Q4. Design your own traffic-light puzzle using three periods that give a joint flash every exactly 2 minutes. Justify your choice.
L6 CreateOne valid design: 20 s, 24 s, 30 s. LCM(20, 24, 30) = 120 s = 2 min. Many answers possible; any triple whose LCM equals 120 works.
Assertion–Reason Questions
Assertion (A): The common multiples of 2 and 5 are exactly the multiples of 10.
Reason (R): The least common multiple of 2 and 5 is 10.
Reason (R): The least common multiple of 2 and 5 is 10.
Answer: (a) — every common multiple of 2 and 5 must be a multiple of their LCM (10), and vice versa.
Assertion (A): 1 is a common factor of every pair of whole numbers.
Reason (R): 1 divides every whole number.
Reason (R): 1 divides every whole number.
Answer: (a) — 1 divides every integer, so 1 is a factor of both numbers in any pair.
Frequently Asked Questions — Prime Time
What is Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool in NCERT Class 6 Mathematics?
Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool is a key concept covered in NCERT Class 6 Mathematics, Chapter 5: Prime Time. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool step by step?
To solve problems on Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 6 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 5: Prime Time?
The essential formulas of Chapter 5 (Prime Time) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool important for the Class 6 board exam?
Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool is part of the NCERT Class 6 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool?
Common mistakes in Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool?
End-of-chapter NCERT exercises for Part 1 — Common Multiples & Common Factors (Idli-Vada Game) | Class 6 Maths | MyAiSchool cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 5, and solve at least one previous-year board paper to consolidate your understanding.
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