Least Common Multiple (LCM) of 71 and 171
The least common multiple (LCM) of 71 and 171 is 12141.
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 171?
First, calculate the GCD of 71 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 171 = 0 remainder 71 |
| 2 | 171 ÷ 71 = 2 remainder 29 |
| 3 | 71 ÷ 29 = 2 remainder 13 |
| 4 | 29 ÷ 13 = 2 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 23 | 4416 |
| 105 and 107 | 11235 |
| 200 and 25 | 200 |
| 185 and 98 | 18130 |
| 69 and 46 | 138 |