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 |
|---|---|
| 132 and 186 | 4092 |
| 113 and 188 | 21244 |
| 189 and 170 | 32130 |
| 162 and 46 | 3726 |
| 90 and 28 | 1260 |