Least Common Multiple (LCM) of 113 and 115
The least common multiple (LCM) of 113 and 115 is 12995.
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 113 and 115?
First, calculate the GCD of 113 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 115 = 0 remainder 113 |
| 2 | 115 ÷ 113 = 1 remainder 2 |
| 3 | 113 ÷ 2 = 56 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 99 | 3069 |
| 17 and 61 | 1037 |
| 109 and 175 | 19075 |
| 179 and 155 | 27745 |
| 194 and 198 | 19206 |