Least Common Multiple (LCM) of 108 and 189
The least common multiple (LCM) of 108 and 189 is 756.
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 189?
First, calculate the GCD of 108 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 189 = 0 remainder 108 |
| 2 | 189 ÷ 108 = 1 remainder 81 |
| 3 | 108 ÷ 81 = 1 remainder 27 |
| 4 | 81 ÷ 27 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 29 | 3393 |
| 51 and 95 | 4845 |
| 130 and 27 | 3510 |
| 106 and 112 | 5936 |
| 78 and 50 | 1950 |