Multiple choice

Numbers are in the ratio of 4 : 5 : 6 and the HCF is 18. Find the LCM.

  1. 1080

  2. 960

  3. 520

  4. 320
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A Correct answer
Explanation

The numbers are 4k, 5k, 6k where k = HCF = 18. The numbers are 72, 90, 108. The LCM of 72, 90, 108 is 1080.

AI explanation

Since the highest common factor is 18, let the numbers be 18x, 18y, and 18z where x, y, and z are coprime. Given the ratio of the numbers is 4 to 5 to 6, we multiply the highest common factor by these ratio parts to find the numbers, which are 72, 90, and 108. The least common multiple is found by taking the highest powers of prime factors present, giving 2^3 * 3^2 * 5, which equals 1080.

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