Least Common Multiple (LCM) of 82 and 139
The least common multiple (LCM) of 82 and 139 is 11398.
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 139?
First, calculate the GCD of 82 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 139 = 0 remainder 82 |
| 2 | 139 ÷ 82 = 1 remainder 57 |
| 3 | 82 ÷ 57 = 1 remainder 25 |
| 4 | 57 ÷ 25 = 2 remainder 7 |
| 5 | 25 ÷ 7 = 3 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 178 | 15664 |
| 19 and 83 | 1577 |
| 197 and 182 | 35854 |
| 159 and 39 | 2067 |
| 14 and 47 | 658 |