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Obviously, they are 6, 12, 18, 24, 30, and 36.

These numbers are the common multiples of 2 and 3 or chole and bhature.
You can play the chole and bhature game with different pairs of numbers like – 2 and 5, 3 and 7 etc.
Moreover, the game can change the word to samosa and pakode or idli and vada or saag and roti, etc.

Example 4: Find the common multiples of 3, 5 and 10.
Solution: Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, ....

Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
Multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, ...

Clearly, common multiples of 3, Note: When you get the first number in common, write the multiples of
5 and 10 are 30, 60, 90,... that common number as common multiples of the given numbers.

Think and Answer

1. At what number is Chole-bhature said for the 8th time?
2. Suppose you play the Chole-bhature game with following pairs of numbers:
(a) 4 and 5 (b) 2 and 7 (c) 6 and 9

Which is the first number for which the players should say, Chole-bhature?
3. Which one of the following is the common multiple of 6, 8 and 12?
(a) 42 (b) 64 (c) 78 (d) 96

Common Factors

A frog is jumping on a number line to catch a grasshopper. If the grasshopper is at 12, can the frog
catch the grasshopper if his jump size is 3?

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
What will happen if the frog increases his jump size to 4?

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
In both the cases, the frog can catch the grasshopper.

What happens when the grasshopper also jumps at 24?
(a) Can the frog still catch the grasshopper if the jump size is 2, 3, 4, 6 or 8?

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

In all the above cases, 24 comes in the multiplication table of 2, 3, 4, 6 and 8, so the frog can
obviously catch the grasshopper.

2 × 12 = 3 × 8 = 4 × 6 = 24

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