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Fundamental Theorem of Arithmetic

A cat jumps 4...

Question

A cat jumps 4 steps at a time while a frog jumps 3 steps at a time. On what step will they land together first if they started at the same time and from the same postion?

A

16th

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B

8th

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C

12th

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D

18th

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Solution

The correct option is C 12th
To find the first common landing step of the cat and frog we need to find the least common multiple of the 4 and 3

multiples of 3 =
3 x 1 = 3
3 x 2 = 6
3 x 3 = 9
3 x 4 = 12
3 x 5 = 15
3 x 6 = 18
3 x 7 = 21
3 x 8 = 24
3 x 9 =27
3 x 10 = 30
Multiples of 4 =
4 x 1 = 4
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24
4 x 7 = 28
4 x 8 = 32
4 x 9 =36
4 x 10 = 40
So LCM of 3 and 4 is 12

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