Least Common Multiple (LCM) of 82 and 157
The least common multiple (LCM) of 82 and 157 is 12874.
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 157?
First, calculate the GCD of 82 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 157 = 0 remainder 82 |
| 2 | 157 ÷ 82 = 1 remainder 75 |
| 3 | 82 ÷ 75 = 1 remainder 7 |
| 4 | 75 ÷ 7 = 10 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 49 | 5684 |
| 53 and 130 | 6890 |
| 21 and 88 | 1848 |
| 57 and 119 | 6783 |
| 127 and 199 | 25273 |