Least Common Multiple (LCM) of 82 and 57
The least common multiple (LCM) of 82 and 57 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 82 and 57?
First, calculate the GCD of 82 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 57 = 1 remainder 25 |
| 2 | 57 ÷ 25 = 2 remainder 7 |
| 3 | 25 ÷ 7 = 3 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 174 | 19662 |
| 148 and 19 | 2812 |
| 176 and 178 | 15664 |
| 160 and 172 | 6880 |
| 165 and 88 | 1320 |