Least Common Multiple (LCM) of 82 and 118
The least common multiple (LCM) of 82 and 118 is 4838.
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 82 and 118?
First, calculate the GCD of 82 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 118 = 0 remainder 82 |
| 2 | 118 ÷ 82 = 1 remainder 36 |
| 3 | 82 ÷ 36 = 2 remainder 10 |
| 4 | 36 ÷ 10 = 3 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 51 | 3417 |
| 45 and 163 | 7335 |
| 169 and 97 | 16393 |
| 200 and 174 | 17400 |
| 178 and 120 | 10680 |