Least Common Multiple (LCM) of 198 and 133
The least common multiple (LCM) of 198 and 133 is 26334.
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 198 and 133?
First, calculate the GCD of 198 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 133 = 1 remainder 65 |
| 2 | 133 ÷ 65 = 2 remainder 3 |
| 3 | 65 ÷ 3 = 21 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 172 | 26316 |
| 136 and 148 | 5032 |
| 165 and 107 | 17655 |
| 54 and 56 | 1512 |
| 20 and 84 | 420 |