Least Common Multiple (LCM) of 47 and 193
The least common multiple (LCM) of 47 and 193 is 9071.
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 47 and 193?
First, calculate the GCD of 47 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 193 = 0 remainder 47 |
| 2 | 193 ÷ 47 = 4 remainder 5 |
| 3 | 47 ÷ 5 = 9 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 155 | 12090 |
| 110 and 120 | 1320 |
| 80 and 181 | 14480 |
| 37 and 197 | 7289 |
| 157 and 70 | 10990 |