Least Common Multiple (LCM) of 130 and 82
The least common multiple (LCM) of 130 and 82 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 130 and 82?
First, calculate the GCD of 130 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 82 = 1 remainder 48 |
| 2 | 82 ÷ 48 = 1 remainder 34 |
| 3 | 48 ÷ 34 = 1 remainder 14 |
| 4 | 34 ÷ 14 = 2 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 20 | 1340 |
| 127 and 50 | 6350 |
| 194 and 31 | 6014 |
| 186 and 117 | 7254 |
| 82 and 138 | 5658 |