Least Common Multiple (LCM) of 199 and 130
The least common multiple (LCM) of 199 and 130 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 199 and 130?
First, calculate the GCD of 199 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 130 = 1 remainder 69 |
| 2 | 130 ÷ 69 = 1 remainder 61 |
| 3 | 69 ÷ 61 = 1 remainder 8 |
| 4 | 61 ÷ 8 = 7 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 190 | 2470 |
| 156 and 117 | 468 |
| 124 and 23 | 2852 |
| 32 and 31 | 992 |
| 147 and 75 | 3675 |