Least Common Multiple (LCM) of 200 and 71
The least common multiple (LCM) of 200 and 71 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 200 and 71?
First, calculate the GCD of 200 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 71 = 2 remainder 58 |
| 2 | 71 ÷ 58 = 1 remainder 13 |
| 3 | 58 ÷ 13 = 4 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 95 | 15485 |
| 95 and 139 | 13205 |
| 25 and 23 | 575 |
| 94 and 61 | 5734 |
| 188 and 67 | 12596 |