The least common multiple (LCM) of 3, 10, and 15 is 30.
To find the LCM, we can use the prime factorization method:
- 3 is a prime number, its factorization is 3.
- 10 can be factored into 2 × 5.
- 15 can be factored into 3 × 5.
Next, we take the highest power of each prime number that appears in these factorizations:
- From 3: 3
- From 10: 2 and 5
- From 15: 5 (but we already counted it)
So the LCM is:
LCM = 21 × 31 × 51 = 2 × 3 × 5 = 30
Thus, the least common multiple of 3, 10, and 15 is 30.