Least Common Multiple (LCM) of 23 and 193
The least common multiple (LCM) of 23 and 193 is 4439.
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 23 and 193?
First, calculate the GCD of 23 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 193 = 0 remainder 23 |
| 2 | 193 ÷ 23 = 8 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 68 | 1564 |
| 113 and 176 | 19888 |
| 100 and 18 | 900 |
| 45 and 110 | 990 |
| 51 and 40 | 2040 |