Least Common Multiple (LCM) of 83 and 183
The least common multiple (LCM) of 83 and 183 is 15189.
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 183?
First, calculate the GCD of 83 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 183 = 0 remainder 83 |
| 2 | 183 ÷ 83 = 2 remainder 17 |
| 3 | 83 ÷ 17 = 4 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 46 | 4278 |
| 120 and 194 | 11640 |
| 146 and 126 | 9198 |
| 109 and 109 | 109 |
| 124 and 177 | 21948 |