Least Common Multiple (LCM) of 118 and 199
The least common multiple (LCM) of 118 and 199 is 23482.
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 118 and 199?
First, calculate the GCD of 118 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 199 = 0 remainder 118 |
| 2 | 199 ÷ 118 = 1 remainder 81 |
| 3 | 118 ÷ 81 = 1 remainder 37 |
| 4 | 81 ÷ 37 = 2 remainder 7 |
| 5 | 37 ÷ 7 = 5 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 45 | 945 |
| 178 and 17 | 3026 |
| 129 and 140 | 18060 |
| 22 and 141 | 3102 |
| 105 and 116 | 12180 |