Least Common Multiple (LCM) of 114 and 182
The least common multiple (LCM) of 114 and 182 is 10374.
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 182?
First, calculate the GCD of 114 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 182 = 0 remainder 114 |
| 2 | 182 ÷ 114 = 1 remainder 68 |
| 3 | 114 ÷ 68 = 1 remainder 46 |
| 4 | 68 ÷ 46 = 1 remainder 22 |
| 5 | 46 ÷ 22 = 2 remainder 2 |
| 6 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 34 | 2074 |
| 58 and 89 | 5162 |
| 123 and 13 | 1599 |
| 180 and 194 | 17460 |
| 189 and 67 | 12663 |