MathDB

LCM(a, b) = 2^r * 3^s

Source: 2023 OLCOMA Costa Rica National Olympiad, Final Round, 3.2

March 20, 2024

number theoryleast common multipleordered pairs

Problem Statement

Find all ordered pairs of positive integers

(r, s)

for which there are exactly

35

ordered pairs of positive integers

(a, b)

such that the least common multiple of

a

and

b

2^r \cdot 3^s