Least Common Multiple (LCM) of 108 and 183
The least common multiple (LCM) of 108 and 183 is 6588.
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 108 and 183?
First, calculate the GCD of 108 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 183 = 0 remainder 108 |
| 2 | 183 ÷ 108 = 1 remainder 75 |
| 3 | 108 ÷ 75 = 1 remainder 33 |
| 4 | 75 ÷ 33 = 2 remainder 9 |
| 5 | 33 ÷ 9 = 3 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 113 | 7119 |
| 120 and 93 | 3720 |
| 187 and 109 | 20383 |
| 191 and 17 | 3247 |
| 83 and 45 | 3735 |