Least Common Multiple (LCM) of 113 and 182
The least common multiple (LCM) of 113 and 182 is 20566.
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 182?
First, calculate the GCD of 113 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 182 = 0 remainder 113 |
| 2 | 182 ÷ 113 = 1 remainder 69 |
| 3 | 113 ÷ 69 = 1 remainder 44 |
| 4 | 69 ÷ 44 = 1 remainder 25 |
| 5 | 44 ÷ 25 = 1 remainder 19 |
| 6 | 25 ÷ 19 = 1 remainder 6 |
| 7 | 19 ÷ 6 = 3 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 59 | 10266 |
| 23 and 91 | 2093 |
| 103 and 21 | 2163 |
| 95 and 25 | 475 |
| 135 and 113 | 15255 |