Least Common Multiple (LCM) of 199 and 131
The least common multiple (LCM) of 199 and 131 is 26069.
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 131?
First, calculate the GCD of 199 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 131 = 1 remainder 68 |
| 2 | 131 ÷ 68 = 1 remainder 63 |
| 3 | 68 ÷ 63 = 1 remainder 5 |
| 4 | 63 ÷ 5 = 12 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 125 | 1000 |
| 123 and 104 | 12792 |
| 116 and 62 | 3596 |
| 71 and 140 | 9940 |
| 43 and 145 | 6235 |