Least Common Multiple (LCM) of 113 and 181
The least common multiple (LCM) of 113 and 181 is 20453.
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 181?
First, calculate the GCD of 113 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 181 = 0 remainder 113 |
| 2 | 181 ÷ 113 = 1 remainder 68 |
| 3 | 113 ÷ 68 = 1 remainder 45 |
| 4 | 68 ÷ 45 = 1 remainder 23 |
| 5 | 45 ÷ 23 = 1 remainder 22 |
| 6 | 23 ÷ 22 = 1 remainder 1 |
| 7 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 140 | 25340 |
| 105 and 17 | 1785 |
| 20 and 146 | 1460 |
| 39 and 144 | 1872 |
| 77 and 179 | 13783 |