The LCM of two positive integers is thrice the larger number. The difference of the smaller number and the HCF of the two numbers is 6. The smaller number is :

Correct option is A

Given:

The LCM of two positive integers = thrice the larger number

Difference between smaller number and HCF = 6

Formula Used:

LCM × HCF = a × b

Substitute the known values and solve.

Solution:

Let the two numbers be a (smaller) and b (larger)

LCM of the two = 3b

3b × HCF = a × b

3 × HCF = a…..(1)

Now,

a – HCF = 6

From(1)

3 × HCF – HCF = 6

2 × HCF = 6

HCF = 3

Now,

3 × 3 = a

a = 9