Least Common Multiple (LCM) of 108 and 132
The least common multiple (LCM) of 108 and 132 is 1188.
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 108 and 132?
First, calculate the GCD of 108 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 132 = 0 remainder 108 |
| 2 | 132 ÷ 108 = 1 remainder 24 |
| 3 | 108 ÷ 24 = 4 remainder 12 |
| 4 | 24 ÷ 12 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 71 | 7597 |
| 143 and 31 | 4433 |
| 68 and 81 | 5508 |
| 116 and 157 | 18212 |
| 189 and 83 | 15687 |