Least Common Multiple (LCM) of 171 and 193
The least common multiple (LCM) of 171 and 193 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 171 and 193?
First, calculate the GCD of 171 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 193 = 0 remainder 171 |
| 2 | 193 ÷ 171 = 1 remainder 22 |
| 3 | 171 ÷ 22 = 7 remainder 17 |
| 4 | 22 ÷ 17 = 1 remainder 5 |
| 5 | 17 ÷ 5 = 3 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 123 | 2706 |
| 64 and 135 | 8640 |
| 72 and 32 | 288 |
| 61 and 113 | 6893 |
| 163 and 176 | 28688 |