Least Common Multiple (LCM) of 107 and 183
The least common multiple (LCM) of 107 and 183 is 19581.
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 107 and 183?
First, calculate the GCD of 107 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 183 = 0 remainder 107 |
| 2 | 183 ÷ 107 = 1 remainder 76 |
| 3 | 107 ÷ 76 = 1 remainder 31 |
| 4 | 76 ÷ 31 = 2 remainder 14 |
| 5 | 31 ÷ 14 = 2 remainder 3 |
| 6 | 14 ÷ 3 = 4 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 37 | 1332 |
| 105 and 84 | 420 |
| 82 and 68 | 2788 |
| 192 and 32 | 192 |
| 102 and 135 | 4590 |