Least Common Multiple (LCM) of 189 and 135
The least common multiple (LCM) of 189 and 135 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 189 and 135?
First, calculate the GCD of 189 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 135 = 1 remainder 54 |
| 2 | 135 ÷ 54 = 2 remainder 27 |
| 3 | 54 ÷ 27 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 63 | 1575 |
| 157 and 126 | 19782 |
| 182 and 73 | 13286 |
| 192 and 20 | 960 |
| 117 and 157 | 18369 |