Least Common Multiple (LCM) of 114 and 120
The least common multiple (LCM) of 114 and 120 is 2280.
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 114 and 120?
First, calculate the GCD of 114 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 120 = 0 remainder 114 |
| 2 | 120 ÷ 114 = 1 remainder 6 |
| 3 | 114 ÷ 6 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 180 | 3420 |
| 21 and 150 | 1050 |
| 12 and 23 | 276 |
| 107 and 67 | 7169 |
| 20 and 100 | 100 |