Multiple choice

What will be the LCM of the numbers whose prime factorisation is expressible as 52 × 33 and 42 × 32?

  1. 540

  2. 10,800

  3. 9720

  4. 3600
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B Correct answer
Explanation

The prime factorizations are 5^2 * 3^3 and 4^2 * 3^2. Since 4^2 = 2^4, the factors are 5^2 * 3^3 and 2^4 * 3^2. The LCM is the product of the highest powers of all prime factors present: 2^4 * 3^3 * 5^2 = 16 * 27 * 25 = 10800.

AI explanation

To find the least common multiple from prime factorizations, take the highest power of each prime present in the numbers. The highest powers are 5 squared, 4 squared and 3 cubed. Multiplying 25 by 16 gives 400, and multiplying 400 by 27 gives 10800. The result is 10800.

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