Hinglish

Common Multiples and Common Factors

Class 6 Maths · Chapter 5: Prime Time · NCERT Ganita Prakash section 5.1

Learn

Multiples of a number are what you get when you count in jumps of that number. Multiples of 4: 4, 8, 12, 16, 20, … They never end!

Clap and snap! Class 6 counts round the room. On every multiple of 4 you clap; on every multiple of 6 you snap; on a number that is a multiple of both, you clap and snap. The first clap-snap comes at 12, then 24, 36 … These are the common multiples of 4 and 6.

4: 4, 8, 12, 16, 20, 24 · 6: 6, 12, 18, 24 → 12, 24

Factors of a number divide it exactly. Arrange 18 tiles into rectangles: 1 × 18, 2 × 9, 3 × 6. So the factors of 18 are 1, 2, 3, 6, 9 and 18.

Meher has a red ribbon 18 cm long and a blue ribbon 24 cm long. She wants to cut both into pieces of the same length, with nothing left over. The piece length must be a common factor of 18 and 24: 1, 2, 3 or 6 cm. The longest pieces she can cut are 6 cm.

common factors: 1, 2, 3, 6

Explore: be a multiple detective on this number board.

  1. Tap every multiple of 5.
  2. Fresh board: tap every common multiple of 4 and 6.
  3. Now find a jump that lands on both 18 and 24. Make it the biggest one you can.

Remember

  • Multiples: count in jumps (4, 8, 12 …). Factors: numbers that divide exactly (factors of 12: 1, 2, 3, 4, 6, 12).
  • Common multiples are in both lists of multiples; common factors are in both lists of factors.

Quick check

Which number is a common multiple of 3 and 5?

  1. 8
  2. 15
  3. 20
  4. 25
Answer

15. 15 = 3 × 5, so it is a multiple of both. 20 and 25 are not multiples of 3.

Think about it

Two numbers, both smaller than 10, have their first common multiple at 35. What are they?

One answer

5 and 7. 35 = 5 × 7, and 5 and 7 have no common factor except 1, so 35 is their first common multiple.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.