Least Common Multiple (LCM) of 135 and 198
The least common multiple (LCM) of 135 and 198 is 2970.
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 135 and 198?
First, calculate the GCD of 135 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 198 = 0 remainder 135 |
| 2 | 198 ÷ 135 = 1 remainder 63 |
| 3 | 135 ÷ 63 = 2 remainder 9 |
| 4 | 63 ÷ 9 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 12 | 204 |
| 36 and 82 | 1476 |
| 41 and 83 | 3403 |
| 19 and 180 | 3420 |
| 122 and 196 | 11956 |