Least Common Multiple (LCM) of 193 and 171
The least common multiple (LCM) of 193 and 171 is 33003.
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 171?
First, calculate the GCD of 193 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 171 = 1 remainder 22 |
| 2 | 171 ÷ 22 = 7 remainder 17 |
| 3 | 22 ÷ 17 = 1 remainder 5 |
| 4 | 17 ÷ 5 = 3 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 50 | 100 |
| 196 and 123 | 24108 |
| 99 and 58 | 5742 |
| 77 and 168 | 1848 |
| 21 and 73 | 1533 |