Least Common Multiple (LCM) of 120 and 180
The least common multiple (LCM) of 120 and 180 is 360.
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 180?
First, calculate the GCD of 120 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 180 = 0 remainder 120 |
| 2 | 180 ÷ 120 = 1 remainder 60 |
| 3 | 120 ÷ 60 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 55 | 3795 |
| 38 and 28 | 532 |
| 10 and 31 | 310 |
| 16 and 178 | 1424 |
| 77 and 140 | 1540 |