Email or username:

Password:

Forgot your password?
Devil Lu Linvega's posts Post Back to profile
Devil Lu Linvega

For two (positive) integers N and M, the properties of their greatest common divisor gcd() and the least common multiple lcm() come in pairs; the phenomenon is partly explained by the formula gcd(M, N) × lcm(M, N) = M × N. 🤯

21 Jul 2022 at 22:15 | Open on merveilles.town
6 comments
curved-ruler

@neauoire of course just think about the prime factorization of M and N

21 Jul 2022 at 22:22 | Open on mastodon.social
Federico I.

@neauoire I also recently found a nice property of GCDs and Fibonacci numbers.

math.hmc.edu/funfacts/fibonacc

21 Jul 2022 at 22:34 | Open on fosstodon.org
Kartik Agaram

@neauoire I can't believe I didn't learn this in school..

22 Jul 2022 at 0:03 | Open on merveilles.town
Leon

@neauoire Are you familiar with how positive integers can be written in the form M = p1^e1 * p2^e2 * ... and N = p1^f1 * p2^f2 * ... where p1, p2, ... are the primes?

A related equation is min(M, N) + max(M, N) = M + N.

If we look at a single prime pi, its exponent is
min(ei, fi) in gcd(M, N),
max(ei, fi) in lcm(M, N)
ei +fi in M*N.

For example with M = 4 = 2^2 * 3^0 and N = 6 = 2^1 * 3^1:

gcd(M, N) = 2 = 2^1 * 3^0
lcm(M, N) = 12 = 2^2 * 3^1
M * N = 24 = 2^(2 + 1) * 3^(0 + 1)

@neauoire Are you familiar with how positive integers can be written in the form M = p1^e1 * p2^e2 * ... and N = p1^f1 * p2^f2 * ... where p1, p2, ... are the primes?

A related equation is min(M, N) + max(M, N) = M + N.

If we look at a single prime pi, its exponent is
min(ei, fi) in gcd(M, N),
max(ei, fi) in lcm(M, N)
ei +fi in M*N.

22 Jul 2022 at 9:07 | Open on merveilles.town
Go Up