Find the smallest perfect square number that is divisible by 6 8 and 18

General
1

find the smallest perfect square number that is divisible by 6 8 and 18

2

To find the smallest perfect square number that is divisible by 6, 8, and 18, we need to find the least common multiple (LCM) of these three numbers.

First, let’s find the prime factorization of each number:

  • 6: 2 * 3
  • 8: 2 * 2 * 2
  • 18: 2 * 3 * 3

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

  • 2^3 * 3^2 = 72

Now, we have 72, but we need to find the smallest perfect square number. To do this, we square the prime factors:

  • 2^4 * 3^2 = 144

Therefore, the smallest perfect square number that is divisible by 6, 8, and 18 is 144.