Least Common Multiple (LCM) of 71 and 200
The least common multiple (LCM) of 71 and 200 is 14200.
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 200?
First, calculate the GCD of 71 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 200 = 0 remainder 71 |
| 2 | 200 ÷ 71 = 2 remainder 58 |
| 3 | 71 ÷ 58 = 1 remainder 13 |
| 4 | 58 ÷ 13 = 4 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 182 | 16380 |
| 27 and 84 | 756 |
| 165 and 90 | 990 |
| 53 and 65 | 3445 |
| 198 and 107 | 21186 |