Least Common Multiple (LCM) of 82 and 130
The least common multiple (LCM) of 82 and 130 is 5330.
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 130?
First, calculate the GCD of 82 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 130 = 0 remainder 82 |
| 2 | 130 ÷ 82 = 1 remainder 48 |
| 3 | 82 ÷ 48 = 1 remainder 34 |
| 4 | 48 ÷ 34 = 1 remainder 14 |
| 5 | 34 ÷ 14 = 2 remainder 6 |
| 6 | 14 ÷ 6 = 2 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 194 | 36278 |
| 198 and 141 | 9306 |
| 84 and 11 | 924 |
| 163 and 33 | 5379 |
| 88 and 87 | 7656 |