MathDB

gcd (a,b)=50! , lcm(a,b)=(50!)^2

Source: 2021 Czech-Polish-Slovak Match Junior, team p3 CPSJ

September 12, 2021

number theorygreatest common divisorleast common multipleLCMGCD

Problem Statement

Find the number of pairs

(a, b)

of positive integers with the property that the greatest common divisor of

a

and

b

is equal to

1\cdot 2 \cdot 3\cdot ... \cdot50

, and the least common multiple of

a

and

b

1^2 \cdot 2^2 \cdot 3^2\cdot ... \cdot 50^2