Question
Three boys step off together from the same place. If their steps measure $36\ cm, 48\ cm$ and $54\ cm$, 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 $= 2 \times 2 \times 3 \times 3 \times 3 \times 2 \times 2 = 16 \times 27 = 432\ cm$
They will step together again at a distance of $432\ cm$ from the starting point
$\begin{array}{c|c}2&36,48,54\\\hline2&18,24,27\\\hline3&9,12,27\\\hline3&3,4,9\\\hline3&1,4,3\\\hline2&1,4,1\\\hline2&1,2,1\\\hline&1,1,1\end{array}$
The required distance $= 2 \times 2 \times 3 \times 3 \times 3 \times 2 \times 2 = 16 \times 27 = 432\ cm$
They will step together again at a distance of $432\ cm$ from the starting point
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Ravish had $20$ pencils, Sikha had $50$ pencils and Priya had $80$ pencils. After $4$ months, Ravish used up $10$ pencils. Shikha used up $25$ pencils and Priya used up $40$ pencils. What fraction did each use up? Check if each has used up an equal fraction of their pencils?
→The following figures have been split into rectangles. Find their areas. (The measures are given in centimetres).
What is the measure of the angle in degrees between:
$i.\ $North and West?
$ii.\ $North and South?
$iii.\ $North and South-East?
→$i.\ $North and West?
$ii.\ $North and South?
$iii.\ $North and South-East?
For the following pairs of numbers, verify the property:
Product of the number = Product of their $H.C.F$ and $L.C.M$
$87,145$
→Product of the number = Product of their $H.C.F$ and $L.C.M$
$87,145$
Following data gives the number of children in $40$ families: $1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2 2, 0, 0, 1, 2, 2, 4, 3, 2,$ $1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2$ Represent it in the form of a frequency distribution.
→Solve these:
| 8 – 13 | (-8) – (13) | (-13) – (-8) | (-13) + (-8) |
| 8 + (-13) | (-8) – (-13) | (13) - 8 | 13 – (-8) |
Solve the following equation by trial and error method: $y + 9 = 13$
→The angles of a triangle are in the ratio $3 : 5 : 7$. Find the measures of these angles.
→How quickly can you do this? Fill the appropriate sign. $('<', '=', '>')$
$\frac{6}{10} \square \frac{3}{5}$
→$\frac{6}{10} \square \frac{3}{5}$
The ratio of zinc and copper in an alloy is $7 : 9$ If the weight of copper in the alloy is $12.6\ kg$ find the weight of zinc in it.
→