Least Common Multiple (LCM) of 114 and 183
The least common multiple (LCM) of 114 and 183 is 6954.
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 114 and 183?
First, calculate the GCD of 114 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 183 = 0 remainder 114 |
| 2 | 183 ÷ 114 = 1 remainder 69 |
| 3 | 114 ÷ 69 = 1 remainder 45 |
| 4 | 69 ÷ 45 = 1 remainder 24 |
| 5 | 45 ÷ 24 = 1 remainder 21 |
| 6 | 24 ÷ 21 = 1 remainder 3 |
| 7 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 163 | 21027 |
| 191 and 77 | 14707 |
| 36 and 200 | 1800 |
| 106 and 70 | 3710 |
| 194 and 30 | 2910 |