Least Common Multiple (LCM) of 157 and 198
The least common multiple (LCM) of 157 and 198 is 31086.
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 157 and 198?
First, calculate the GCD of 157 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 198 = 0 remainder 157 |
| 2 | 198 ÷ 157 = 1 remainder 41 |
| 3 | 157 ÷ 41 = 3 remainder 34 |
| 4 | 41 ÷ 34 = 1 remainder 7 |
| 5 | 34 ÷ 7 = 4 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 54 | 7398 |
| 116 and 142 | 8236 |
| 196 and 128 | 6272 |
| 75 and 34 | 2550 |
| 79 and 143 | 11297 |