Least Common Multiple (LCM) of 19 and 17
The least common multiple (LCM) of 19 and 17 is 323.
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 19 and 17?
First, calculate the GCD of 19 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 17 = 1 remainder 2 |
| 2 | 17 ÷ 2 = 8 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 189 | 24759 |
| 131 and 15 | 1965 |
| 45 and 20 | 180 |
| 135 and 146 | 19710 |
| 112 and 47 | 5264 |