The HCF and LCM of two numbers is 14 and 588 respectively. If the first number is 84, find the second one?

Question

LCM of two numbers is 60 times their HCF. If sum of LCM and HCF is 549. If one number is 45 then what is the other number?

Answer 1

Let the 2 numbers be a & b.
a = 84 = 2^2 × 3 × 7
b = ? = 2 × 7 × y { because LCM = 14 = 2 × 7 }
HCF = 588 = 2^2 × 7 × 3 × y
y = 588/(4 × 7 × 3) = 7
Therefore b = 2 × 7^2 = 98