Find the least square number, exactly divisible by each one of the numbers: (i) 6,9, 15 and 20) (ii) 8,12, 15 and 20
(i) 6, 9, 15 and 20
L.C.M of given 4 numbers is 180
180 = 22 × 32 × 5
To make it a perfect square, we have to multiply the number with 5
Therefore,
180 × 5 = 22 × 32 × 52
900 is the least square number divisible by 6, 9, 15 and 20
3600 is the least square number divisible by 8, 12, 15 and 20
(ii) 8, 2, 15 and 20
L.C.M of given 4 numbers is 360
360 = 22 × 32 ×2 × 5
To make it a perfect square, we have to multiply the number with 2 × 5 = 10
Therefore,
360 × 10 = 22 × 32 × 52 × 22