Least Common Multiple (LCM) of 80 and 171
The least common multiple (LCM) of 80 and 171 is 13680.
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 80 and 171?
First, calculate the GCD of 80 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 171 = 0 remainder 80 |
| 2 | 171 ÷ 80 = 2 remainder 11 |
| 3 | 80 ÷ 11 = 7 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 134 | 2814 |
| 123 and 161 | 19803 |
| 85 and 81 | 6885 |
| 114 and 159 | 6042 |
| 169 and 192 | 32448 |