Least Common Multiple (LCM) of 17 and 200
The least common multiple (LCM) of 17 and 200 is 3400.
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 200?
First, calculate the GCD of 17 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 200 = 0 remainder 17 |
| 2 | 200 ÷ 17 = 11 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 |
|---|---|
| 56 and 170 | 4760 |
| 57 and 143 | 8151 |
| 10 and 63 | 630 |
| 196 and 173 | 33908 |
| 13 and 190 | 2470 |