Question : Three numbers are in the ratio 2 : 3 : 5 and their LCM is 60. What is the HCF of the numbers?
Option 1: 2
Option 2: 4
Option 3: 10
Option 4: 6
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Correct Answer: 2
Solution : Given, Three numbers are in the ratio 2 : 3 : 5 and their LCM is 60. Let the number be $2x$, $3x$, and $5x$. ⇒ LCM of ($2x$, $3x$ and $5x$) $=2 × 3 × 5 × x=30x$ According to the question $30x = 60$ ⇒ $x = 2$ ⇒ The numbers are 4, 6, and 10. Now, 4 = 2 × 2 6 = 2 × 3 10 = 2 × 5 $\therefore$ HCF of 4, 6, and 10 = 2 Hence, the correct answer is 2.
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