Least Common Multiple (LCM) of 71 and 199
The least common multiple (LCM) of 71 and 199 is 14129.
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 71 and 199?
First, calculate the GCD of 71 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 199 = 0 remainder 71 |
| 2 | 199 ÷ 71 = 2 remainder 57 |
| 3 | 71 ÷ 57 = 1 remainder 14 |
| 4 | 57 ÷ 14 = 4 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 181 | 25702 |
| 197 and 50 | 9850 |
| 200 and 135 | 5400 |
| 33 and 67 | 2211 |
| 129 and 146 | 18834 |