Least Common Multiple (LCM) of 83 and 189
The least common multiple (LCM) of 83 and 189 is 15687.
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 83 and 189?
First, calculate the GCD of 83 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 189 = 0 remainder 83 |
| 2 | 189 ÷ 83 = 2 remainder 23 |
| 3 | 83 ÷ 23 = 3 remainder 14 |
| 4 | 23 ÷ 14 = 1 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 168 | 2184 |
| 18 and 189 | 378 |
| 71 and 172 | 12212 |
| 30 and 177 | 1770 |
| 95 and 74 | 7030 |