Least Common Multiple (LCM) of 15 and 24
The least common multiple (LCM) of 15 and 24 is 120.
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 15 and 24?
First, calculate the GCD of 15 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 24 = 0 remainder 15 |
| 2 | 24 ÷ 15 = 1 remainder 9 |
| 3 | 15 ÷ 9 = 1 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 71 | 12780 |
| 70 and 97 | 6790 |
| 129 and 197 | 25413 |
| 95 and 53 | 5035 |
| 113 and 16 | 1808 |