Least Common Multiple (LCM) of 137 and 198
The least common multiple (LCM) of 137 and 198 is 27126.
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 137 and 198?
First, calculate the GCD of 137 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 198 = 0 remainder 137 |
| 2 | 198 ÷ 137 = 1 remainder 61 |
| 3 | 137 ÷ 61 = 2 remainder 15 |
| 4 | 61 ÷ 15 = 4 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 57 | 1824 |
| 107 and 183 | 19581 |
| 165 and 27 | 1485 |
| 103 and 83 | 8549 |
| 69 and 161 | 483 |