Least Common Multiple (LCM) of 198 and 107
The least common multiple (LCM) of 198 and 107 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 198 and 107?
First, calculate the GCD of 198 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 107 = 1 remainder 91 |
| 2 | 107 ÷ 91 = 1 remainder 16 |
| 3 | 91 ÷ 16 = 5 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 75 | 10650 |
| 75 and 108 | 2700 |
| 115 and 125 | 2875 |
| 27 and 56 | 1512 |
| 51 and 85 | 255 |