Least Common Multiple (LCM) of 82 and 185
The least common multiple (LCM) of 82 and 185 is 15170.
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 185?
First, calculate the GCD of 82 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 185 = 0 remainder 82 |
| 2 | 185 ÷ 82 = 2 remainder 21 |
| 3 | 82 ÷ 21 = 3 remainder 19 |
| 4 | 21 ÷ 19 = 1 remainder 2 |
| 5 | 19 ÷ 2 = 9 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 139 | 22518 |
| 109 and 191 | 20819 |
| 65 and 166 | 10790 |
| 124 and 38 | 2356 |
| 30 and 137 | 4110 |