Question

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

Answer 1

Length of Rod1 = 45cm

Length of Rod2= 50cm

Length of Rod3 = 75cm

Now,

Converting all in metres:-

Rod1 = 0.45m

Rod2 = 0.5m

Rod3= 0.75m

Now,

To get the length of the rope which can be measured completely by each of these three rods, we need to find the Least Common Multiple or LCM of the three rods.

Hence,

LCM of 45,50,75 will be :-

5| 45, 50,75

5| 9, 10,15

3|9, 2, 3

3| 3, 2, 1

2|1,2,1

1,1,1

Hence,

LCM will be 450cm

Thus, the length of the rope required will be 4.5 metres.

(since, 1 metre = 100 centimeters)