Least Common Multiple (LCM) of 21 and 15
The least common multiple (LCM) of 21 and 15 is 105.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 21 and 15?
First, calculate the GCD of 21 and 15 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 15 = 1 remainder 6 |
| 2 | 15 ÷ 6 = 2 remainder 3 |
| 3 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 117 | 2340 |
| 156 and 66 | 1716 |
| 24 and 17 | 408 |
| 196 and 185 | 36260 |
| 92 and 23 | 92 |