Least Common Multiple (LCM) of 193 and 173
The least common multiple (LCM) of 193 and 173 is 33389.
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 193 and 173?
First, calculate the GCD of 193 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 173 = 1 remainder 20 |
| 2 | 173 ÷ 20 = 8 remainder 13 |
| 3 | 20 ÷ 13 = 1 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 38 | 3192 |
| 13 and 132 | 1716 |
| 136 and 144 | 2448 |
| 123 and 117 | 4797 |
| 20 and 91 | 1820 |