Least Common Multiple (LCM) of 189 and 133
The least common multiple (LCM) of 189 and 133 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 189 and 133?
First, calculate the GCD of 189 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 133 = 1 remainder 56 |
| 2 | 133 ÷ 56 = 2 remainder 21 |
| 3 | 56 ÷ 21 = 2 remainder 14 |
| 4 | 21 ÷ 14 = 1 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 23 | 1863 |
| 88 and 29 | 2552 |
| 32 and 26 | 416 |
| 133 and 195 | 25935 |
| 31 and 44 | 1364 |