Least Common Multiple (LCM) of 107 and 198
The least common multiple (LCM) of 107 and 198 is 21186.
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 107 and 198?
First, calculate the GCD of 107 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 198 = 0 remainder 107 |
| 2 | 198 ÷ 107 = 1 remainder 91 |
| 3 | 107 ÷ 91 = 1 remainder 16 |
| 4 | 91 ÷ 16 = 5 remainder 11 |
| 5 | 16 ÷ 11 = 1 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 150 | 900 |
| 43 and 54 | 2322 |
| 117 and 89 | 10413 |
| 157 and 180 | 28260 |
| 187 and 54 | 10098 |