Least Common Multiple (LCM) of 182 and 113
The least common multiple (LCM) of 182 and 113 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 182 and 113?
First, calculate the GCD of 182 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 182 ÷ 113 = 1 remainder 69 |
| 2 | 113 ÷ 69 = 1 remainder 44 |
| 3 | 69 ÷ 44 = 1 remainder 25 |
| 4 | 44 ÷ 25 = 1 remainder 19 |
| 5 | 25 ÷ 19 = 1 remainder 6 |
| 6 | 19 ÷ 6 = 3 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 180 | 3420 |
| 181 and 155 | 28055 |
| 195 and 187 | 36465 |
| 172 and 78 | 6708 |
| 178 and 113 | 20114 |