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
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.
$\begin{array}{c|c}2&36,48,54\\\hline2&18,24,27\\\hline3&9,12,27\\\hline3&3,4,9\\\hline3&1,4,3\\\hline2&1,4,1\\\hline2&1,2,1\\\hline&1,1,1\end{array}$
The required distance = 2 × 2 × 3 × 3 × 3 × 2 × 2
= 16 × 27
= 432cm
They will step together again at a distance of 432cm from the starting point
The least distance from the starting point where they will step together will be given by the LCM of 36, 48 and 54.
$\begin{array}{c|c}2&36,48,54\\\hline2&18,24,27\\\hline3&9,12,27\\\hline3&3,4,9\\\hline3&1,4,3\\\hline2&1,4,1\\\hline2&1,2,1\\\hline&1,1,1\end{array}$
The required distance = 2 × 2 × 3 × 3 × 3 × 2 × 2
= 16 × 27
= 432cm
They will step together again at a distance of 432cm from the starting point
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