Least Common Multiple (LCM) of 114 and 82
The least common multiple (LCM) of 114 and 82 is 4674.
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 82?
First, calculate the GCD of 114 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 82 = 1 remainder 32 |
| 2 | 82 ÷ 32 = 2 remainder 18 |
| 3 | 32 ÷ 18 = 1 remainder 14 |
| 4 | 18 ÷ 14 = 1 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 17 | 918 |
| 61 and 130 | 7930 |
| 56 and 46 | 1288 |
| 166 and 92 | 7636 |
| 168 and 199 | 33432 |