Least Common Multiple (LCM) of 189 and 108
The least common multiple (LCM) of 189 and 108 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 189 and 108?
First, calculate the GCD of 189 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 108 = 1 remainder 81 |
| 2 | 108 ÷ 81 = 1 remainder 27 |
| 3 | 81 ÷ 27 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 15 | 1005 |
| 175 and 109 | 19075 |
| 108 and 96 | 864 |
| 180 and 66 | 1980 |
| 111 and 83 | 9213 |