Least Common Multiple (LCM) of 47 and 108
The least common multiple (LCM) of 47 and 108 is 5076.
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 108?
First, calculate the GCD of 47 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 108 = 0 remainder 47 |
| 2 | 108 ÷ 47 = 2 remainder 14 |
| 3 | 47 ÷ 14 = 3 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 28 | 140 |
| 122 and 60 | 3660 |
| 39 and 80 | 3120 |
| 197 and 35 | 6895 |
| 13 and 132 | 1716 |