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 |
|---|---|
| 60 and 106 | 3180 |
| 12 and 97 | 1164 |
| 119 and 130 | 15470 |
| 84 and 66 | 924 |
| 137 and 46 | 6302 |