Least Common Multiple (LCM) of 42 and 193
The least common multiple (LCM) of 42 and 193 is 8106.
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 42 and 193?
First, calculate the GCD of 42 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 193 = 0 remainder 42 |
| 2 | 193 ÷ 42 = 4 remainder 25 |
| 3 | 42 ÷ 25 = 1 remainder 17 |
| 4 | 25 ÷ 17 = 1 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 54 | 3186 |
| 149 and 200 | 29800 |
| 195 and 57 | 3705 |
| 20 and 162 | 1620 |
| 135 and 189 | 945 |