Least Common Multiple (LCM) of 82 and 189
The least common multiple (LCM) of 82 and 189 is 15498.
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 82 and 189?
First, calculate the GCD of 82 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 189 = 0 remainder 82 |
| 2 | 189 ÷ 82 = 2 remainder 25 |
| 3 | 82 ÷ 25 = 3 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 15 | 480 |
| 190 and 42 | 3990 |
| 128 and 49 | 6272 |
| 180 and 189 | 3780 |
| 150 and 181 | 27150 |