Least Common Multiple (LCM) of 125 and 108
The least common multiple (LCM) of 125 and 108 is 13500.
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 125 and 108?
First, calculate the GCD of 125 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 108 = 1 remainder 17 |
| 2 | 108 ÷ 17 = 6 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 66 | 330 |
| 144 and 59 | 8496 |
| 96 and 112 | 672 |
| 10 and 43 | 430 |
| 150 and 197 | 29550 |