Multiple choice

The LCM of two positive numbers exceeds their HCF by 875. Their LCM is 36 times their HCF. If the smaller number is 25, then find the larger number?

  1. 900

  2. 950

  3. 1000

  4. 1050
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A Correct answer
Explanation

Let H be the HCF. LCM = 36H. Given LCM - H = 875, so 35H = 875, H = 25. The numbers are 25 and x. Since HCF is 25, the numbers must be multiples of 25. LCM = (25 * x) / 25 = x. So x = 36 * 25 = 900.

AI explanation

Let the HCF be h, so the LCM is 36h. The difference between the LCM and HCF is 36h minus h, which equals 35h. We are given this difference is 875, so 35h equals 875 and h is 25. The product of two numbers equals their LCM multiplied by their HCF, so 25 multiplied by the larger number equals 900 multiplied by 25. Solving this gives the larger number as 900.

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