Least Common Multiple (LCM) of 103 and 193
The least common multiple (LCM) of 103 and 193 is 19879.
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 193?
First, calculate the GCD of 103 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 193 = 0 remainder 103 |
| 2 | 193 ÷ 103 = 1 remainder 90 |
| 3 | 103 ÷ 90 = 1 remainder 13 |
| 4 | 90 ÷ 13 = 6 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 193 | 34161 |
| 135 and 11 | 1485 |
| 40 and 45 | 360 |
| 197 and 15 | 2955 |
| 178 and 34 | 3026 |