Question

PLEASE ANSWER WILL GIVE BRAINLIEST!!!!!! m and n are positive integers greater than 1. The product of GCD and LCM of the integers is 143. Find m + n.

Answer 1

Answer:

We see that it is always possible to write both M and N as the products of the same prime factors, albeit with different exponents. Some of the exponents will need to be zero.

Now, both GCD(M, N) and LCM(M, N) are products of the same prime factors where the exponents in G are the least of the corresponding two, whilst in L they are the largest:

GCD(M, N) = p min(a, α) q min(b, β)· ... · r min(c, γ),

LCM(M, N) = p max(a, α) q max(b, β)· ... · r max(c, γ).

Now, (2) thus insures that (1) holds. To continue the example:

GCD(12, 10) = 213050 = 2,

LCM(12, 10) = 223151 = 60.

Naturally, 12×10 = 2×60.

Step-by-step explanation: