Least Common Multiple (LCM) of 189 and 132
The least common multiple (LCM) of 189 and 132 is 8316.
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 132?
First, calculate the GCD of 189 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 132 = 1 remainder 57 |
| 2 | 132 ÷ 57 = 2 remainder 18 |
| 3 | 57 ÷ 18 = 3 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 86 | 4816 |
| 11 and 38 | 418 |
| 180 and 80 | 720 |
| 122 and 185 | 22570 |
| 16 and 23 | 368 |