Discussion
A frog jumps 3 steps and a rabbit jumps 7 steps at a time starting from a place O. At which of the following steps, they both will be jumping together ?
Answer: C
They will jump together at step 378.
The frog lands on multiples of 3 and the rabbit on multiples of 7, so they meet only on common multiples of 3 and 7, that is, multiples of their LCM, 21.
\[ 378 = 21 \times 18 \]
The others fail one test: 343 = 7 × 49 and 371 = 7 × 53 are multiples of 7 but not of 3 (digit sums 10 and 11), while 354 is a multiple of 3 but not of 7.
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