Least Common Multiple (LCM) of 105 and 183
The least common multiple (LCM) of 105 and 183 is 6405.
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 105 and 183?
First, calculate the GCD of 105 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 183 = 0 remainder 105 |
| 2 | 183 ÷ 105 = 1 remainder 78 |
| 3 | 105 ÷ 78 = 1 remainder 27 |
| 4 | 78 ÷ 27 = 2 remainder 24 |
| 5 | 27 ÷ 24 = 1 remainder 3 |
| 6 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 60 | 1860 |
| 112 and 43 | 4816 |
| 190 and 40 | 760 |
| 135 and 153 | 2295 |
| 100 and 84 | 2100 |