Least Common Multiple (LCM) of 130 and 83
The least common multiple (LCM) of 130 and 83 is 10790.
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 83?
First, calculate the GCD of 130 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 83 = 1 remainder 47 |
| 2 | 83 ÷ 47 = 1 remainder 36 |
| 3 | 47 ÷ 36 = 1 remainder 11 |
| 4 | 36 ÷ 11 = 3 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 17 | 272 |
| 74 and 199 | 14726 |
| 61 and 24 | 1464 |
| 109 and 156 | 17004 |
| 41 and 10 | 410 |