Least Common Multiple (LCM) of 113 and 89
The least common multiple (LCM) of 113 and 89 is 10057.
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 89?
First, calculate the GCD of 113 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 89 = 1 remainder 24 |
| 2 | 89 ÷ 24 = 3 remainder 17 |
| 3 | 24 ÷ 17 = 1 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 71 | 13064 |
| 65 and 22 | 1430 |
| 192 and 95 | 18240 |
| 127 and 89 | 11303 |
| 84 and 175 | 2100 |