Least Common Multiple (LCM) of 120 and 50
The least common multiple (LCM) of 120 and 50 is 600.
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 50?
First, calculate the GCD of 120 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 50 = 2 remainder 20 |
| 2 | 50 ÷ 20 = 2 remainder 10 |
| 3 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 142 | 13632 |
| 13 and 197 | 2561 |
| 45 and 126 | 630 |
| 89 and 85 | 7565 |
| 116 and 86 | 4988 |