Least Common Multiple (LCM) of 17 and 47
The least common multiple (LCM) of 17 and 47 is 799.
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 17 and 47?
First, calculate the GCD of 17 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 47 = 0 remainder 17 |
| 2 | 47 ÷ 17 = 2 remainder 13 |
| 3 | 17 ÷ 13 = 1 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 20 | 500 |
| 169 and 74 | 12506 |
| 126 and 25 | 3150 |
| 92 and 53 | 4876 |
| 129 and 134 | 17286 |