3.2

Part of 2023 Costa Rica - Final Round

Problems(1)

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

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

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

b

2^r \cdot 3^s

number theoryleast common multipleordered pairs