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

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

The sum of two numbers is 384 and

t heir GCD is 48 . What is the LCM of

the numbers ?

Commented by 1549442205PVT last updated on 22/Jul/20

Similar to Q 104413

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

g c d (x, y) = 48

\Rightarrow x = 48 m

\Rightarrow y = 48 n

w i t h g c d (m, n) = 1 \dots (i)

x + y = 48 (m + n) = 384

\Rightarrow m + n = 8 \dots (i i)

l c m (x, y) = 48 \times l c m (m, n)

c a s e 1 : m = 1, n = 7 o r m = 7, n = 1

l c m (x, y) = 48 \times l c m (1, 7) = 336

c a s e 2 : m = 3, n = 5 o r m = 5, n = 3

l c m (x, y) = 48 \times l c m (3, 5) = 720

s o t h e a n s w e r i s 336 o r 720 .

Commented by Rasheed.Sindhi last updated on 22/Jul/20

G \overset{R}{} E \overset{A}{} T!