What is the least perfect square exactly divisible by each of the numbers 6,9,15 and 20 ?

Question

What is the least perfect square exactly divisible by each of the numbers 6,9,15 and 20 ? (A) 3600 (B) 400 (C) 900 (D) 225

Tardigrade Admin · Accepted Answer

L.C.M. of (6,9,15. and 20) =180=22 × 32 × 5 So to make it a perfect square we have to multiply it by 5 . ∴ Least perfect square =22 × 32 × 52 Exactly divisible by 6, 9, 15 and 20=900

Q. What is the least perfect square exactly divisible by each of the numbers $6, 9, 15$ and 20 ?

3600

400

900

225

L.C.M. of $(6, 9, 15$ and 20) $= 180 = 2^{2} \times 3^{2} \times 5$
So to make it a perfect square we have to multiply it by 5 .
$∴$ Least perfect square $= 2^{2} \times 3^{2} \times 5^{2}$
Exactly divisible by 6, 9, 15 and $20 = 900$

Q. What is the least perfect square exactly divisible by each of the numbers 6,9,15 and 20 ?

3600

400

900

225

L.C.M. of (6,9,15 and 20) =180=22×32×5 So to make it a perfect square we have to multiply it by 5 . ∴ Least perfect square =22×32×52 Exactly divisible by 6, 9, 15 and 20=900

Q. What is the least perfect square exactly divisible by each of the numbers $6, 9, 15$ and 20 ?

L.C.M. of $(6, 9, 15$ and 20) $= 180 = 2^{2} \times 3^{2} \times 5$
So to make it a perfect square we have to multiply it by 5 .
$∴$ Least perfect square $= 2^{2} \times 3^{2} \times 5^{2}$
Exactly divisible by 6, 9, 15 and $20 = 900$