Question

Three boys step off together from the same place. If their steps measure $36cm$, $48cm$ and $54cm$, at what distance from the starting point will they again step together?

Answer 1

From the starting point, they will step together again when they travel a distance that is exactly divisible by the lengths of their steps.
The least distance from the starting point where they will step together will be given by the LCM of $36,48$ and $54$.

$36=2^2\times 3^2$

$48=2^4\times 3$

$54=2\times 3^3$

LCM $=$ The product of highest common prime factors

$\Rightarrow$ LCM $(36,48,54)=2^4\times 3^3$

$\Rightarrow$ LCM $(36,48,54)=16\times 27=432$
Therefore, they will step together again at a distance of $432cm$ from the starting point.