Least Common Multiple (LCM) of 183 and 114
The least common multiple (LCM) of 183 and 114 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 183 and 114?
First, calculate the GCD of 183 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 183 ÷ 114 = 1 remainder 69 |
| 2 | 114 ÷ 69 = 1 remainder 45 |
| 3 | 69 ÷ 45 = 1 remainder 24 |
| 4 | 45 ÷ 24 = 1 remainder 21 |
| 5 | 24 ÷ 21 = 1 remainder 3 |
| 6 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 14 | 1260 |
| 140 and 81 | 11340 |
| 49 and 10 | 490 |
| 21 and 126 | 126 |
| 188 and 174 | 16356 |