Question

The greatest common factor of 2 numbers is 10. The least common multiple of these same 2
numbers is 120. What are the two numbers?

Answer 1

Answer:

2 and 5are commander factor of 10

Answer 2

The numbers are 30 and 40.

Given:

The greatest common factor of the 2 numbers is 10. The least common multiple of these same 2

numbers are 120.

To Find:

The two numbers.

Solution:

To find the two numbers we will follow the following steps:

Let the two numbers be 10 and 10y because 10 is the highest common factor of the numbers.

As we know,

The product of the LCM and HCF of the two numbers is equal to the product of the two numbers.

So,

$10x \times 10y = 120 \times 10 = 1200$

$xy = \frac{1200}{100} = 12$

x and y can be 3,4, and 6,2 but the least common factor is 120 will be obtained from the 3 and 4.

So,

Numbers are: 10x = 10×3 = 30 and 10y = 10×4 = 40

Henceforth, the numbers are 30 and 40.

#SPJ2