Question : The ratio of the two numbers is 5 : 7 and their HCF is 3. Their LCM is:
Option 1: 75
Option 2: 105
Option 3: 125
Option 4: 35
Correct Answer: 105
Solution :
The two numbers are in the ratio 5 : 7, and their highest common factor (HCF) is 3. Therefore, the numbers are 5 × 3 = 15 and 7 × 3 = 21.
The least common multiple (LCM) of two numbers is given by the product of the two numbers divided by their HCF. So, the LCM of 15 and 21 is:
LCM = $\frac{15 \times 21}{3}$ = 105
Hence, the correct answer is 105.
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