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
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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