Least Common Multiple (LCM) of 17 and 19
The least common multiple (LCM) of 17 and 19 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 17 and 19?
First, calculate the GCD of 17 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 19 = 0 remainder 17 |
| 2 | 19 ÷ 17 = 1 remainder 2 |
| 3 | 17 ÷ 2 = 8 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 74 | 10730 |
| 152 and 138 | 10488 |
| 159 and 193 | 30687 |
| 26 and 16 | 208 |
| 43 and 200 | 8600 |