Least Common Multiple (LCM) of 115 and 89
The least common multiple (LCM) of 115 and 89 is 10235.
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 89?
First, calculate the GCD of 115 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 89 = 1 remainder 26 |
| 2 | 89 ÷ 26 = 3 remainder 11 |
| 3 | 26 ÷ 11 = 2 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 32 | 1184 |
| 122 and 13 | 1586 |
| 135 and 189 | 945 |
| 183 and 119 | 21777 |
| 70 and 20 | 140 |