Least Common Multiple (LCM) of 133 and 198
The least common multiple (LCM) of 133 and 198 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 133 and 198?
First, calculate the GCD of 133 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 198 = 0 remainder 133 |
| 2 | 198 ÷ 133 = 1 remainder 65 |
| 3 | 133 ÷ 65 = 2 remainder 3 |
| 4 | 65 ÷ 3 = 21 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 43 | 1247 |
| 142 and 72 | 5112 |
| 34 and 125 | 4250 |
| 74 and 160 | 5920 |
| 116 and 80 | 2320 |