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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

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Best 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

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