MathDB
MMO 021 Moscow MO 1935 lcm , gcd of 2 and 3 numbers

Source:

July 17, 2019
least common multiplegreatest common divisornumber theory

Problem Statement

Denote by M(a,b,c,...,k)M(a, b, c, . . . , k) the least common multiple and by D(a,b,c,...,k)D(a, b, c, . . . , k) the greatest common divisor of a,b,c,...,ka, b, c, . . . , k. Prove that:
a) M(a,b)D(a,b)=abM(a, b)D(a, b) = ab,
b) M(a,b,c)D(a,b)D(b,c)D(a,c)D(a,b,c)=abc\frac{M(a, b, c)D(a, b)D(b, c)D(a, c)}{D(a, b, c)}= abc.
Back to ProblemsView on AoPS