Least Common Multiple (LCM) of 82 and 159
The least common multiple (LCM) of 82 and 159 is 13038.
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 159?
First, calculate the GCD of 82 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 159 = 0 remainder 82 |
| 2 | 159 ÷ 82 = 1 remainder 77 |
| 3 | 82 ÷ 77 = 1 remainder 5 |
| 4 | 77 ÷ 5 = 15 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 117 | 3393 |
| 165 and 71 | 11715 |
| 86 and 197 | 16942 |
| 98 and 22 | 1078 |
| 106 and 91 | 9646 |