Question

find the least number which is a perfect square and which is also divisible by 16, 18 and 45. plz answer fast I will mark u as brainliest.

Answer 1

the least no. which is divisible by 16,18,45 is the L.C.M. of 16,18,and 45 which is 2×2×2×2×3×3×5
making pairs,(2×2)×(2×2)×(3×3)×5
we find that 5 remains unpaired
hence it should be multiplied by 5 to make it a perfect square
hence the least no. that is a perfect sq. and also divisible by 16,18 and 45 is
(2×2)×(2×2)×(3×3)×(5×5) that is 3600

Answer 2

In order to find the least number, we need to do the LCM of 16,18 and 45.

Prime factorization of 16 = 2^4

Prime factorization of 18 = 2 * 3 * 3

Prime factorization of 45 = 3 * 3 * 5

LCM(16,18,45) = 2^4 * 3^2 * 5

= 720.

As we can see here, 5 is not in pair. So, we need to multiply 720 by 5 to make it a perfect square.

= > 720 * 5

= > 3600.

Therefore, the least perfect square number = 3600.

Hope this helps!