Question

the sum of two numbers is 135 and their HCF is 27 if the LCM 162 what are the numbers?

Answer 1

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Answer 2

The two numbers are 54 and 81.

Given: The sum of two numbers is 135 and their HCF is 27 if the LCM 162.

To find: We have to find the numbers.

Solution:

The HCF between the two numbers is 27.

So, let the two numbers be 27x and 27y.

Now given that sum of the two numbers is 135.

So, we can write-

$27x + 27y = 135 \\ x + y = 5$

Now again given that the LCM of the two numbers are 162.

So, we can write-

$27xy = 162 \\ xy = 6$

Thus x and y can be 3 and 2 or vice versa.

So, the two numbers are 54 and 81.