Find the least square number, exactly divisible by each one of the num

1.	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
Answer» (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

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

Answer»

(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