The LCM of two numbers is 12 times their HCF. One of the numbers is 8 and the sum of the HCF and LCM is 52. What is the other number?

Correct option is B

Given:

One number is 8

LCM of two number is 12 times their HCF

Sum of their HCF and LCM =52

Formula Used:

Product of two numbers = HCF$$\times$$​ LCM

Solution:

Let the HCF be x

Then LCM =$$12 \times x = 12x$$​​

Now $$x+12x = 52$$​​

​$$13x= 52$$​​

​$$x=4$$​​

HCF = 4

LCM = $$12x = 48$$​​

One of the number is 8

Let the other number is y

Then $$8 \times y = 4 \times 48$$​​

y = 24 

Thus, the other number is 24