Least Common Multiple (LCM) of 132 and 180
The least common multiple (LCM) of 132 and 180 is 1980.
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 132 and 180?
First, calculate the GCD of 132 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 180 = 0 remainder 132 |
| 2 | 180 ÷ 132 = 1 remainder 48 |
| 3 | 132 ÷ 48 = 2 remainder 36 |
| 4 | 48 ÷ 36 = 1 remainder 12 |
| 5 | 36 ÷ 12 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 127 | 14732 |
| 81 and 30 | 810 |
| 150 and 45 | 450 |
| 114 and 105 | 3990 |
| 166 and 112 | 9296 |