Least Common Multiple (LCM) of 135 and 189
The least common multiple (LCM) of 135 and 189 is 945.
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 135 and 189?
First, calculate the GCD of 135 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 189 = 0 remainder 135 |
| 2 | 189 ÷ 135 = 1 remainder 54 |
| 3 | 135 ÷ 54 = 2 remainder 27 |
| 4 | 54 ÷ 27 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 54 | 1080 |
| 65 and 79 | 5135 |
| 152 and 26 | 1976 |
| 180 and 50 | 900 |
| 110 and 157 | 17270 |