Least Common Multiple (LCM) of 126 and 183
The least common multiple (LCM) of 126 and 183 is 7686.
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 126 and 183?
First, calculate the GCD of 126 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 183 = 0 remainder 126 |
| 2 | 183 ÷ 126 = 1 remainder 57 |
| 3 | 126 ÷ 57 = 2 remainder 12 |
| 4 | 57 ÷ 12 = 4 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 169 | 33124 |
| 61 and 61 | 61 |
| 46 and 129 | 5934 |
| 10 and 25 | 50 |
| 116 and 113 | 13108 |