Least Common Multiple (LCM) of 115 and 71
The least common multiple (LCM) of 115 and 71 is 8165.
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 71?
First, calculate the GCD of 115 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 71 = 1 remainder 44 |
| 2 | 71 ÷ 44 = 1 remainder 27 |
| 3 | 44 ÷ 27 = 1 remainder 17 |
| 4 | 27 ÷ 17 = 1 remainder 10 |
| 5 | 17 ÷ 10 = 1 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 141 | 3102 |
| 23 and 56 | 1288 |
| 177 and 102 | 6018 |
| 60 and 17 | 1020 |
| 167 and 55 | 9185 |