Least Common Multiple (LCM) of 47 and 109
The least common multiple (LCM) of 47 and 109 is 5123.
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 109?
First, calculate the GCD of 47 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 109 = 0 remainder 47 |
| 2 | 109 ÷ 47 = 2 remainder 15 |
| 3 | 47 ÷ 15 = 3 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 38 | 2736 |
| 39 and 32 | 1248 |
| 198 and 170 | 16830 |
| 181 and 19 | 3439 |
| 153 and 130 | 19890 |