L.C.M of two numbers is 156 and their H.C.F is 2. If the sum of the numbers is 38, then what is their difference?

Question

The L.C.M and H.C.F of two numbers are 336 and 12 respectively.
If one of the number is 84 then what will be the other number?

Answer 1

a + b = 38
a × b = H.C.F × L.C.M = 156 × 2 = 312
(a + b )^2 - (a - b)^2 = 4ab
(a - b) = ((a + b)^2 - 4ab)^(0.5) = ((38^2) - (4 × 312))^0.5 = 14
a = 26 & b = 12.