## anonymous 5 years ago Can someone explain what is the difference between LCM and GCD. When should I use them.

1. anonymous

least common multiple the smallest number that both numbers can multiply to ie 2, 4 would have a LCM of 4 you would use this to find the common denominators of fractions for add/sub great common divisor something along the line of greatest common factor ie 6, 9 would have a GCD of 3 you would use GCD when you are simplifying fractions, or just simplifying in general

2. anonymous

LCM of two numbers say a and b is divisible by both of the numbers like if LCM(a, b) = k, then a/k and b/k GCD of two numbers divides both of the numbers if GCD (a,b) = m, then m/a and m/b

3. anonymous

the same definition can be extended ro more than two numbers

4. anonymous

also we have product of numbers = LCM*GCD

5. anonymous

Ahh If I dont missundertand you LCM is used when we want to get rid of fractions. And we use GCD when we are simplifying terms. A I right?

6. anonymous

LCM isn't for getting rid of fractions when you add fractions you want to have the same denominator, you usually want the LCM as the denominator ie the LCM of 2, 3 is 6 $\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

7. anonymous

does that make sense?

8. anonymous

Yeah. Can you give me an example with GCD please?

9. anonymous

sure so if you're trying to simplify the fraction $\frac{12}{18}$ the GCD of 12 and 18 is 6 so you divide both the numerator and the denominator by 6 to get $\frac{2}{3}$ make sense?

10. anonymous

Yeah completely. Your are really got at this Chiaroscuro. +10 for you

11. anonymous

lol thanks