Question : The LCM of the two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the numbers is 100, then the other number is:
Option 1: 5
Option 2: 25
Option 3: 100
Option 4: 125
Correct Answer: 25
Solution :
Let LCM = L and HCF = H, then
Given: L = 4H
The sum of LCM and HCF = 125
⇒ H + 4H = 125
⇒ 5H = 125
⇒ H =$\frac{125}{5}$
⇒ H = 25
∴ L = 4 × 25 = 100
2
nd
number = $\frac{L× H}{100}$ = $\frac{100× 25}{100}$ = 25
Hence, the correct answer is 25.
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