Least Common Multiple (LCM) of 34 and 193
The least common multiple (LCM) of 34 and 193 is 6562.
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 34 and 193?
First, calculate the GCD of 34 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 193 = 0 remainder 34 |
| 2 | 193 ÷ 34 = 5 remainder 23 |
| 3 | 34 ÷ 23 = 1 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 142 | 8236 |
| 176 and 30 | 2640 |
| 171 and 55 | 9405 |
| 109 and 200 | 21800 |
| 66 and 192 | 2112 |