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 |
|---|---|
| 99 and 37 | 3663 |
| 87 and 11 | 957 |
| 92 and 167 | 15364 |
| 109 and 92 | 10028 |
| 39 and 140 | 5460 |