Least Common Multiple (LCM) of 127 and 198
The least common multiple (LCM) of 127 and 198 is 25146.
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 127 and 198?
First, calculate the GCD of 127 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 198 = 0 remainder 127 |
| 2 | 198 ÷ 127 = 1 remainder 71 |
| 3 | 127 ÷ 71 = 1 remainder 56 |
| 4 | 71 ÷ 56 = 1 remainder 15 |
| 5 | 56 ÷ 15 = 3 remainder 11 |
| 6 | 15 ÷ 11 = 1 remainder 4 |
| 7 | 11 ÷ 4 = 2 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 160 | 25120 |
| 108 and 50 | 2700 |
| 21 and 128 | 2688 |
| 21 and 12 | 84 |
| 199 and 143 | 28457 |