Question

The LCM of two numbers is 7 times their HCF. The sum of LCM and HCF is 240. find
the two numbers.​

Answer 1

Answer:

I think answer is 3150@@@@

Answer 2

Given info : The LCM of two numbers is 7 times their HCF and the sum of LCM and HCF is 240.

To find : The two numbers are ..

solution : let HCF of two numbers is m.

we know, HCF of numbers is highest common factor among them.

so we can assume , two numbers ma and mb where a and b are co - prime numbers.

using formula,

HCF × LCM = product of numbers

⇒ m × 7m = ma × mb

[ as LCM is 7 times of their HCF. ]

⇒7 = ab

now we can assume a = 1 , b = 7 [ because a and b are co - prime numbers ]

again, sum of HCF and LCM = 240

⇒m + 7m = 240

⇒m = 30

now numbers are ; ma = 30 × 1 = 30 and mb = 30 × 7 = 210

Therefore the numbers are 30 and 210