Question

What strategies could you use to solve this problem? The school choir practices Christmas carols every 3 days and holiday hymns every 5 days. They practiced both today. In how many days will they practice both again?

Answer 1

You need the least common multiple (LCM) of 3 and 5 — the smallest positive number that is a multiple of both.

Strategies:

1. Listing multiples:
- Multiples of 3: 3, 6, 9, 12, 15, ...
- Multiples of 5: 5, 10, 15, ...
- First common multiple is 15 → in 15 days.

2. Use gcd/LCM formula:
- gcd(3,5) = 1, so LCM = 3×5 / 1 = 15.

3. Modular arithmetic:
- Find smallest n>0 with n ≡ 0 (mod 3) and n ≡ 0 (mod 5). That means n ≡ 0 (mod 15), so n = 15.

So they will practice both again in 15 days (counting today as day 0).