Question

Three numbers are in the ratio of 6:7:3 and their LCM is 3654. Their HCF is:

• A. 28
• B. 87
• C. 29
• D. 27

Answer 1

Answer:

B. 87

Let the three numbers be:
6x,; 7x,; 3x

Use relation between LCM and HCF

For numbers in ratio form:
$\text{LCM} = x \times \text{LCM of }(6,7,3)$

LCM of (6, 7, 3 = 42)

So,
$3654 = x \times 42$
$x = \frac{3654}{42} = 87$

Find HCF

$\text{HCF} = x \times \text{HCF of }(6,7,3)$

HCF of (6, 7, 3 = 1)

$\text{HCF} = 87 \times 1 = 87$