Least Common Multiple (LCM) of 199 and 120
The least common multiple (LCM) of 199 and 120 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 199 and 120?
First, calculate the GCD of 199 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 120 = 1 remainder 79 |
| 2 | 120 ÷ 79 = 1 remainder 41 |
| 3 | 79 ÷ 41 = 1 remainder 38 |
| 4 | 41 ÷ 38 = 1 remainder 3 |
| 5 | 38 ÷ 3 = 12 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 167 | 15030 |
| 153 and 24 | 1224 |
| 72 and 28 | 504 |
| 60 and 123 | 2460 |
| 29 and 40 | 1160 |