Least Common Multiple (LCM) of 120 and 125
The least common multiple (LCM) of 120 and 125 is 3000.
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 120 and 125?
First, calculate the GCD of 120 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 125 = 0 remainder 120 |
| 2 | 125 ÷ 120 = 1 remainder 5 |
| 3 | 120 ÷ 5 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 112 | 4592 |
| 57 and 145 | 8265 |
| 126 and 63 | 126 |
| 80 and 68 | 1360 |
| 131 and 13 | 1703 |