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 _______
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:
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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
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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)
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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.
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