I saw in a book that we can find the LCM and GCD of three numbers using prime factorization . That was really cool :) I'll explain what i saw and will let you know my doubt in the end!
Three numbers 12,15,18
LCM = Highest power of the all the factors
GCD = Lowest power of the shared factor
12 can be prime factorized as 3 * 2^2
15 can be prime factorized as 3 * 5
21 can be prime factorized as 2 * 3^2
So GCD =3 since that is the only number common in three number factorizations.
LCM = 2^2 * 3 * 5 = 60
And the answer looks good !!
My doubt is how this gives the correct answer(proof of correctness) ?
I am expecting a simple explanation with example so that i can understand easily :)
Thanks in advance !!