Least Common Multiple (LCM) of 171 and 109
The least common multiple (LCM) of 171 and 109 is 18639.
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 109?
First, calculate the GCD of 171 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 109 = 1 remainder 62 |
| 2 | 109 ÷ 62 = 1 remainder 47 |
| 3 | 62 ÷ 47 = 1 remainder 15 |
| 4 | 47 ÷ 15 = 3 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 164 | 3444 |
| 113 and 135 | 15255 |
| 37 and 78 | 2886 |
| 75 and 20 | 300 |
| 193 and 170 | 32810 |