Least Common Multiple (LCM) of 130 and 199
The least common multiple (LCM) of 130 and 199 is 25870.
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 199?
First, calculate the GCD of 130 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 199 = 0 remainder 130 |
| 2 | 199 ÷ 130 = 1 remainder 69 |
| 3 | 130 ÷ 69 = 1 remainder 61 |
| 4 | 69 ÷ 61 = 1 remainder 8 |
| 5 | 61 ÷ 8 = 7 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 133 | 10374 |
| 81 and 172 | 13932 |
| 77 and 56 | 616 |
| 68 and 53 | 3604 |
| 57 and 82 | 4674 |