Least Common Multiple (LCM) of 82 and 61
The least common multiple (LCM) of 82 and 61 is 5002.
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 61?
First, calculate the GCD of 82 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 61 = 1 remainder 21 |
| 2 | 61 ÷ 21 = 2 remainder 19 |
| 3 | 21 ÷ 19 = 1 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 178 | 16376 |
| 102 and 175 | 17850 |
| 56 and 168 | 168 |
| 172 and 51 | 8772 |
| 181 and 25 | 4525 |