Question

The gcd of two numbers is 17 and their lcm is 204. one of the numbers is 68. find the other number.

Answer 1

$x\cdot y=GCD(x,\ y)\cdot LCM(x,\ y)\\\\\text{We have}\\\\x=68,\ GCD=17,\ LCM=204.\\\\\text{Substitute:}\\\\68y=(17)(204)\\\\68y=3,468\qquad\text{divide both sides by 68}\\\\\boxed{y=51}\\\\Answer:\ \boxed{\text{The other number is 51.}}$