Least Common Multiple (LCM) of 57 and 82
The least common multiple (LCM) of 57 and 82 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 57 and 82?
First, calculate the GCD of 57 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 82 = 0 remainder 57 |
| 2 | 82 ÷ 57 = 1 remainder 25 |
| 3 | 57 ÷ 25 = 2 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 59 | 5900 |
| 13 and 77 | 1001 |
| 72 and 46 | 1656 |
| 170 and 123 | 20910 |
| 14 and 99 | 1386 |