Least Common Multiple (LCM) of 163 and 193
The least common multiple (LCM) of 163 and 193 is 31459.
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 163 and 193?
First, calculate the GCD of 163 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 193 = 0 remainder 163 |
| 2 | 193 ÷ 163 = 1 remainder 30 |
| 3 | 163 ÷ 30 = 5 remainder 13 |
| 4 | 30 ÷ 13 = 2 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 53 | 1219 |
| 165 and 66 | 330 |
| 109 and 46 | 5014 |
| 180 and 10 | 180 |
| 78 and 64 | 2496 |