Least Common Multiple (LCM) of 47 and 111
The least common multiple (LCM) of 47 and 111 is 5217.
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 111?
First, calculate the GCD of 47 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 111 = 0 remainder 47 |
| 2 | 111 ÷ 47 = 2 remainder 17 |
| 3 | 47 ÷ 17 = 2 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 37 | 6290 |
| 47 and 200 | 9400 |
| 33 and 96 | 1056 |
| 196 and 189 | 5292 |
| 179 and 111 | 19869 |