discrete math

If a and b are positive integers, prove that:
ab = gcd(a,b)*lcm(a,b).

Can visualize this being true and easily create examples just don't know how to prove algebraically.

well the gcd of any two number can be found by multiplying the two numbers together and the lcm of all numbers is
Thus ab = gcd(a,b)*lcm(a,b)
= (a*b)* 1
= ab

The lcd is usally the number we try to find so the gcd is never really stressed, unless you are teaching students how to compare fractions quickly when simplified fractions isn't necessary. For example:

7/8 and 9/11
set them up as ratios and cross multiply
77 and 72...the reason this works is because you basically found the gcd of 88 but since the denominators are both 88 it isn't relevant in the comparison

This is an incorrect answer as your first line, gcd "can be found multiplying the two numbers together" is wrong.

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