Question

The ratio of the sum to the lcm of two natural numbers is 7:12. if their hcf is 4, then find the smaller number.

Answer 1

The small number will be 12

Answer 2

Answer:

Smaller number = 12

Step-by-step explanation:

Given : The ratio of the sum to the lcm of two natural numbers is 7:12. If their hcf is 4.

To find : The smaller number.

Solution :

Since, HCF = 4

So, let the numbers be 4x and 4y are prime.

The LCM of the two numbers is 4xy

According to question,

The ratio of the sum to the LCM of two natural numbers is 7:12.

$\frac{4x+4y}{4xy}=\frac{7}{12}$

$\frac{x+y}{xy}=\frac{7}{12}$

$12(x+y)=7xy$

$12(x+y)=7xy$

The numbers are x = 3, y = 4 which satisfy the above condition.

Substitute the value in the numbers,

4x=4(3)=12

4y=4(4)=16

Smaller number is 12.