Question

Three measuring rods are of lengths 120 cm, 100 cm and 150 cm. Find the least length of a fence that can be measured an exact number of times, using any of the rods. How many times each rod will be used to measure the length of the fence?

Answer 1

Length of rod 1 = 120 cm

Length of rod 2 = 100 cm

Length of rod 3 = 150 cm

The prime factorization of 120, 100 and 150 are

100 = 2² × 5²

120 = 2³ × 3 × 5

150 = 2 × 3 × 5²

LCM (120, 100, 150) = 2³ × 3 × 5²

= 8 × 3 × 25

= 600

Time taken by rods to measure the length of the fence:

By rod 1 : `600/120` = 5 times

By rod 2 : `600/100` = 6 times

By rod 3 : `600/150` = 4 times

The least length of the fence is 600 cm and the rods will be used 5, 6, 4 times, respectively.