Least Common Multiple (LCM) of 182 and 107
The least common multiple (LCM) of 182 and 107 is 19474.
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 107?
First, calculate the GCD of 182 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 182 ÷ 107 = 1 remainder 75 |
| 2 | 107 ÷ 75 = 1 remainder 32 |
| 3 | 75 ÷ 32 = 2 remainder 11 |
| 4 | 32 ÷ 11 = 2 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 177 | 1947 |
| 105 and 144 | 5040 |
| 139 and 156 | 21684 |
| 40 and 141 | 5640 |
| 199 and 129 | 25671 |