Find the least square number which is exactly divisible by each of the

1.	Find the least square number which is exactly divisible by each of the numbers 6, 9, 15 and 20.
Answer» Given numbers = 6, 9, 15 and 20 The smallest number divisible by 6, 9, 15 and 20 is their L.C.M. i.e. 180 Resolving the L.C.M. as prime factors we get, 180= 2 × 2 × 3 × 3 × 5 To make it perfect square multiply by 5 then it becomes, 180= 2 × 2 × 3 × 3 × 5 × 5 Which implies 180 × 5 = 900 Least square number which is exactly divisible by 6, 9, 15 and 20 is 900.

Find the least square number which is exactly divisible by each of the numbers 6, 9, 15 and 20.

Answer»

Given numbers = 6, 9, 15 and 20

The smallest number divisible by 6, 9, 15 and 20 is their L.C.M. i.e. 180

Resolving the L.C.M. as prime factors we get, 180= 2 × 2 × 3 × 3 × 5

To make it perfect square multiply by 5 then it becomes, 180= 2 × 2 × 3 × 3 × 5 × 5

Which implies 180 × 5 = 900

Least square number which is exactly divisible by 6, 9, 15 and 20 is 900.