Least Common Multiple (LCM) of 83 and 163
The least common multiple (LCM) of 83 and 163 is 13529.
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 163?
First, calculate the GCD of 83 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 163 = 0 remainder 83 |
| 2 | 163 ÷ 83 = 1 remainder 80 |
| 3 | 83 ÷ 80 = 1 remainder 3 |
| 4 | 80 ÷ 3 = 26 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 175 | 12775 |
| 64 and 126 | 4032 |
| 130 and 150 | 1950 |
| 14 and 189 | 378 |
| 55 and 197 | 10835 |