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 |
|---|---|
| 198 and 104 | 10296 |
| 101 and 61 | 6161 |
| 147 and 167 | 24549 |
| 108 and 144 | 432 |
| 116 and 173 | 20068 |