Least Common Multiple (LCM) of 83 and 181
The least common multiple (LCM) of 83 and 181 is 15023.
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 83 and 181?
First, calculate the GCD of 83 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 181 = 0 remainder 83 |
| 2 | 181 ÷ 83 = 2 remainder 15 |
| 3 | 83 ÷ 15 = 5 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 41 | 7872 |
| 114 and 76 | 228 |
| 85 and 199 | 16915 |
| 197 and 179 | 35263 |
| 43 and 196 | 8428 |