Least Common Multiple (LCM) of 120 and 108
The least common multiple (LCM) of 120 and 108 is 1080.
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 108?
First, calculate the GCD of 120 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 108 = 1 remainder 12 |
| 2 | 108 ÷ 12 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 96 | 288 |
| 29 and 16 | 464 |
| 61 and 28 | 1708 |
| 118 and 57 | 6726 |
| 189 and 36 | 756 |