Least Common Multiple (LCM) of 171 and 89
The least common multiple (LCM) of 171 and 89 is 15219.
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 89?
First, calculate the GCD of 171 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 89 = 1 remainder 82 |
| 2 | 89 ÷ 82 = 1 remainder 7 |
| 3 | 82 ÷ 7 = 11 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 114 | 1254 |
| 181 and 61 | 11041 |
| 163 and 96 | 15648 |
| 72 and 31 | 2232 |
| 172 and 62 | 5332 |