Least Common Multiple (LCM) of 171 and 71
The least common multiple (LCM) of 171 and 71 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 171 and 71?
First, calculate the GCD of 171 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 71 = 2 remainder 29 |
| 2 | 71 ÷ 29 = 2 remainder 13 |
| 3 | 29 ÷ 13 = 2 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 185 | 23495 |
| 154 and 90 | 6930 |
| 128 and 32 | 128 |
| 75 and 25 | 75 |
| 15 and 35 | 105 |