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### Question

The sum of LCM and HCF of two numbers is 150 and LCM is 24 times the HCF. If one of the two numbers is 144, then the other number is?

**A**

6.

**B**

8.

**C**

7.

**D**

9.

**Soln.**

**Ans: a**

Let L be the LCM, and H the HCF. Then H + L = 150, and L = 24H. Solving these for H, we get H = $150/{24 + 1}$ = 6, and L = 144. The product of the two numbers is equal to the product of the lcm and hcf = 6 × 144 = 864. The other number is 864/144 = 6.