Find Greatest Common Divisor and Least Common Multiple

Question

Find GCD (320, 112) and LCM[320, 112].

Solve the equation 320x + 112y = a in the following situations:

(i) a = 32

(ii) a = 10.

Using Euclids Algorithm to find the GCD I have the following:

320 = 112*2 + 96 112 = 96*1 + 16 96 = 16*6 + 0

GCD(320, 112) = 16

(edit) Okay, after working a bit I remembered how to find LCM with prime factors

320 = 2^6 * 5 112 = 2^4 * 7

So, LCM[320, 112] = (2^6)(5)(7) = 2240

Moving on, I need to know how to apply this information to solve the equations.

You have the relationship $\operatorname{lcm}(a,b) \gcd(a,b) = |ab|$. — copper.hat, Oct 09 '13 at 15:49

score 1 · Accepted Answer · answered Oct 09 '13 at 15:06

1

(i) In the first case : $$320x + 112y = 32$$ Which is an equation of a line and has infinite solutions for $(x,y)$

(ii)Similar explanation.

answered Oct 09 '13 at 15:06

rnjai

1 Answers1