Least Common Multiple (LCM) of 138 and 198
The least common multiple (LCM) of 138 and 198 is 4554.
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 138 and 198?
First, calculate the GCD of 138 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 198 = 0 remainder 138 |
| 2 | 198 ÷ 138 = 1 remainder 60 |
| 3 | 138 ÷ 60 = 2 remainder 18 |
| 4 | 60 ÷ 18 = 3 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 164 | 3116 |
| 22 and 177 | 3894 |
| 155 and 43 | 6665 |
| 163 and 124 | 20212 |
| 126 and 38 | 2394 |