Least Common Multiple (LCM) of 120 and 132
The least common multiple (LCM) of 120 and 132 is 1320.
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 120 and 132?
First, calculate the GCD of 120 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 132 = 0 remainder 120 |
| 2 | 132 ÷ 120 = 1 remainder 12 |
| 3 | 120 ÷ 12 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 67 | 5025 |
| 105 and 193 | 20265 |
| 194 and 191 | 37054 |
| 96 and 158 | 7584 |
| 54 and 109 | 5886 |