Least Common Multiple (LCM) of 183 and 107
The least common multiple (LCM) of 183 and 107 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 183 and 107?
First, calculate the GCD of 183 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 183 ÷ 107 = 1 remainder 76 |
| 2 | 107 ÷ 76 = 1 remainder 31 |
| 3 | 76 ÷ 31 = 2 remainder 14 |
| 4 | 31 ÷ 14 = 2 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 180 | 4500 |
| 42 and 130 | 2730 |
| 178 and 88 | 7832 |
| 98 and 35 | 490 |
| 132 and 45 | 1980 |