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 |
|---|---|
| 96 and 13 | 1248 |
| 90 and 15 | 90 |
| 13 and 13 | 13 |
| 149 and 21 | 3129 |
| 13 and 138 | 1794 |