Least Common Multiple (LCM) of 199 and 118
The least common multiple (LCM) of 199 and 118 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 199 and 118?
First, calculate the GCD of 199 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 118 = 1 remainder 81 |
| 2 | 118 ÷ 81 = 1 remainder 37 |
| 3 | 81 ÷ 37 = 2 remainder 7 |
| 4 | 37 ÷ 7 = 5 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 21 | 966 |
| 71 and 188 | 13348 |
| 195 and 28 | 5460 |
| 139 and 106 | 14734 |
| 158 and 116 | 9164 |