Least Common Multiple (LCM) of 103 and 163
The least common multiple (LCM) of 103 and 163 is 16789.
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 103 and 163?
First, calculate the GCD of 103 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 163 = 0 remainder 103 |
| 2 | 163 ÷ 103 = 1 remainder 60 |
| 3 | 103 ÷ 60 = 1 remainder 43 |
| 4 | 60 ÷ 43 = 1 remainder 17 |
| 5 | 43 ÷ 17 = 2 remainder 9 |
| 6 | 17 ÷ 9 = 1 remainder 8 |
| 7 | 9 ÷ 8 = 1 remainder 1 |
| 8 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 84 | 1596 |
| 164 and 89 | 14596 |
| 113 and 171 | 19323 |
| 123 and 142 | 17466 |
| 56 and 149 | 8344 |