Least Common Multiple (LCM) of 115 and 171
The least common multiple (LCM) of 115 and 171 is 19665.
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 115 and 171?
First, calculate the GCD of 115 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 171 = 0 remainder 115 |
| 2 | 171 ÷ 115 = 1 remainder 56 |
| 3 | 115 ÷ 56 = 2 remainder 3 |
| 4 | 56 ÷ 3 = 18 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 75 | 8400 |
| 20 and 21 | 420 |
| 125 and 82 | 10250 |
| 164 and 197 | 32308 |
| 169 and 104 | 1352 |