Least Common Multiple (LCM) of 108 and 135
The least common multiple (LCM) of 108 and 135 is 540.
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 135?
First, calculate the GCD of 108 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 135 = 0 remainder 108 |
| 2 | 135 ÷ 108 = 1 remainder 27 |
| 3 | 108 ÷ 27 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 110 | 2200 |
| 166 and 192 | 15936 |
| 192 and 80 | 960 |
| 12 and 143 | 1716 |
| 80 and 21 | 1680 |