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LCM of 23×3×52 3 ×3×5 and 24×5×72 4 ×5×7 is _______

Question

LCM of 23×3×52 3 ×3×5 and 24×5×72 4 ×5×7 is _______

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Solution

The question seems to be a bit unclear, but I'm assuming you're asking for the Least Common Multiple (LCM) of the numbers 23×3×52, 3×3×5, and 24×5×72.

Here are the steps to find the LCM:

  1. First, break down each number into its prime factors:

    • 23×3×52 = 2^3 * 3 * 5^2
    • 3×3×5 = 3^2 * 5
    • 24×5×72 = 2^4 * 5 * 7^2
  2. Then, for each prime number, take the highest power that appears in any of the factorizations.

    • For 2, the highest power is 4 (from 24×5×72)
    • For 3, the highest power is 2 (from 3×3×5)
    • For 5, the highest power is 2 (from 23×3×52)
    • For 7, the highest power is 2 (from 24×5×72)
  3. Multiply these highest powers together to get the LCM:

    • LCM = 2^4 * 3^2 * 5^2 * 7^2

So, the LCM of 23×3×52, 3×3×5, and 24×5×72 is 2^4 * 3^2 * 5^2 * 7^2.

This problem has been solved

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