Question

Three measuring rods are 45 cm, 50 cm and 75 cm in length. What is the least length (in metres) of a rope that can be measured by the full length of each of these three rods?

Answer 1

The length of the required rope must be such that it is exactly divisible by 45, 50 and 75. The least length will be given by the LCM of 45, 50 and 75.

$\begin{array}{l}2\overline{)45,50,75}\\ 3\overline{)45,25,75}\\ 3\overline{)15,25,25}\\ 5\overline{)5,25,25}\\ 5\overline{)1,5,5}\\ \text{1,1,1}\end{array}$

Required length = 3 × 3 ×5 × 5 × 2
= 450 cm
So, the minimum length of the rope that can be measured by the full length of each of the three rods is 450 cm.