Least Common Multiple (LCM) of 13 and 163
The least common multiple (LCM) of 13 and 163 is 2119.
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 13 and 163?
First, calculate the GCD of 13 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 163 = 0 remainder 13 |
| 2 | 163 ÷ 13 = 12 remainder 7 |
| 3 | 13 ÷ 7 = 1 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 34 | 6494 |
| 55 and 175 | 1925 |
| 52 and 81 | 4212 |
| 48 and 187 | 8976 |
| 77 and 57 | 4389 |