Least Common Multiple (LCM) of 91 and 115
The least common multiple (LCM) of 91 and 115 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 91 and 115?
First, calculate the GCD of 91 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 115 = 0 remainder 91 |
| 2 | 115 ÷ 91 = 1 remainder 24 |
| 3 | 91 ÷ 24 = 3 remainder 19 |
| 4 | 24 ÷ 19 = 1 remainder 5 |
| 5 | 19 ÷ 5 = 3 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 111 | 6438 |
| 180 and 193 | 34740 |
| 12 and 65 | 780 |
| 61 and 126 | 7686 |
| 46 and 198 | 4554 |