Least Common Multiple (LCM) of 171 and 82
The least common multiple (LCM) of 171 and 82 is 14022.
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 82?
First, calculate the GCD of 171 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 82 = 2 remainder 7 |
| 2 | 82 ÷ 7 = 11 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 56 | 9688 |
| 167 and 191 | 31897 |
| 114 and 180 | 3420 |
| 186 and 121 | 22506 |
| 154 and 73 | 11242 |