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 |
|---|---|
| 81 and 143 | 11583 |
| 68 and 157 | 10676 |
| 146 and 47 | 6862 |
| 90 and 148 | 6660 |
| 182 and 29 | 5278 |