Least Common Multiple (LCM) of 50 and 120
The least common multiple (LCM) of 50 and 120 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 50 and 120?
First, calculate the GCD of 50 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 120 = 0 remainder 50 |
| 2 | 120 ÷ 50 = 2 remainder 20 |
| 3 | 50 ÷ 20 = 2 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 14 | 574 |
| 154 and 102 | 7854 |
| 180 and 87 | 5220 |
| 59 and 124 | 7316 |
| 139 and 37 | 5143 |