Question

(ii) Find the least length of a rope which can be cut into whole number of pieces of lengths 45 cm, 75 cm and 81 cm.

Answer 1

Given length of pieces - 45 cm, 75 cm and 81 cm

To find the length of the rope we have to find the L.C.M. of 45, 75 and 81.
      
     __________________
 3  |  45, 75, 81
     |________________     
 3  |  15, 25, 27
     |________________
 3  |    5, 25,  9
     |________________
 3  |    5, 25,  3
     |________________
 5  |    5, 25,  1
     |________________
 5  |    1,  5,   1
     |________________
     |    1, 1,   1
     |

L.C.M. = 3*3*3*3*5*5
= 2025 cm

So, the least length of the rope should be 2025 cm which can be cut into whole number of pieces of length 45 cm, 75 cm and 81 cm.