# The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, find the other.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

When the LCM of two numbers is 14 times their HCF and they have a sum of 600, If one number is 280, then the other number is 80. It is important to find out the HCF and LCM before calculating the rest of the answer. HCF refers to the highest common factor and LCM refers to the least common multiple.

## LCM of two numbers is 14 times their HCF and they have a sum 600

To find out the two numbers that will give out LCM which is 14 times HCF with sum of 600, we will follow the below-mentioned steps.

Now, Let the HCF be h and LCM be 14h

HCF+LCM = 600

First number = 280

So now,

h+ 14h=600

15h= 600

h= 600/15

h= 40

HCF= 40

LCM = 14h = 14×40 = 560

LCM = 560

Now, we will calculate the second number in the following way.

HCF×LCM = first number × second number

Let the second number be s.

40×560 = 280×s

s = (40×560) /280

s = 40×2

s = 80

Hence, the second number required along with 280 is 80.

Summary:

## The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, find the other.

If the LCM of two numbers is 14 times their HCF with a sum of 600 and the first number is 280, then the second number is 80. Candidates can calculate this by finding out the values of HCF and LCM first and then using them to find the value of the second number.

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