Least Common Multiple (LCM) of 115 and 81
The least common multiple (LCM) of 115 and 81 is 9315.
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 81?
First, calculate the GCD of 115 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 81 = 1 remainder 34 |
| 2 | 81 ÷ 34 = 2 remainder 13 |
| 3 | 34 ÷ 13 = 2 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 113 | 16046 |
| 103 and 22 | 2266 |
| 145 and 190 | 5510 |
| 82 and 129 | 10578 |
| 160 and 178 | 14240 |