Least Common Multiple (LCM) of 47 and 17
The least common multiple (LCM) of 47 and 17 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 47 and 17?
First, calculate the GCD of 47 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 17 = 2 remainder 13 |
| 2 | 17 ÷ 13 = 1 remainder 4 |
| 3 | 13 ÷ 4 = 3 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 176 | 17072 |
| 138 and 56 | 3864 |
| 103 and 117 | 12051 |
| 61 and 105 | 6405 |
| 136 and 25 | 3400 |