Least Common Multiple (LCM) of 133 and 189
The least common multiple (LCM) of 133 and 189 is 3591.
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 189?
First, calculate the GCD of 133 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 189 = 0 remainder 133 |
| 2 | 189 ÷ 133 = 1 remainder 56 |
| 3 | 133 ÷ 56 = 2 remainder 21 |
| 4 | 56 ÷ 21 = 2 remainder 14 |
| 5 | 21 ÷ 14 = 1 remainder 7 |
| 6 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 100 | 14300 |
| 100 and 114 | 5700 |
| 22 and 60 | 660 |
| 55 and 71 | 3905 |
| 49 and 92 | 4508 |