Least Common Multiple (LCM) of 120 and 199
The least common multiple (LCM) of 120 and 199 is 23880.
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 199?
First, calculate the GCD of 120 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 199 = 0 remainder 120 |
| 2 | 199 ÷ 120 = 1 remainder 79 |
| 3 | 120 ÷ 79 = 1 remainder 41 |
| 4 | 79 ÷ 41 = 1 remainder 38 |
| 5 | 41 ÷ 38 = 1 remainder 3 |
| 6 | 38 ÷ 3 = 12 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 165 | 4785 |
| 71 and 71 | 71 |
| 148 and 200 | 7400 |
| 18 and 87 | 522 |
| 12 and 78 | 156 |