Least Common Multiple (LCM) of 113 and 86
The least common multiple (LCM) of 113 and 86 is 9718.
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 86?
First, calculate the GCD of 113 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 86 = 1 remainder 27 |
| 2 | 86 ÷ 27 = 3 remainder 5 |
| 3 | 27 ÷ 5 = 5 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 25 | 2900 |
| 83 and 77 | 6391 |
| 19 and 35 | 665 |
| 57 and 109 | 6213 |
| 126 and 52 | 3276 |