Least Common Multiple (LCM) of 115 and 91
The least common multiple (LCM) of 115 and 91 is 10465.
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 91?
First, calculate the GCD of 115 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 91 = 1 remainder 24 |
| 2 | 91 ÷ 24 = 3 remainder 19 |
| 3 | 24 ÷ 19 = 1 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 179 | 1790 |
| 15 and 25 | 75 |
| 36 and 121 | 4356 |
| 63 and 104 | 6552 |
| 78 and 162 | 2106 |