Question Number 104536 by Anindita last updated on 22/Jul/20

The sum of two numbers is 384 and  their GCD is 48. What is the LCM of  the numbers ?

Commented by1549442205PVT last updated on 22/Jul/20

Similar to Q104413

Answered by mr W last updated on 22/Jul/20

gcd(x,y)=48  ⇒x=48m  ⇒y=48n  with gcd(m,n)=1   ...(i)  x+y=48(m+n)=384  ⇒m+n=8   ...(ii)  lcm(x,y)=48×lcm(m,n)    case 1: m=1,n=7 or m=7, n=1  lcm(x,y)=48×lcm(1,7)=336  case 2: m=3,n=5 or m=5, n=3  lcm(x,y)=48×lcm(3,5)=720    so the answer is 336 or 720.

Commented byRasheed.Sindhi last updated on 22/Jul/20

G^(R) E^(A) T  !