Least Common Multiple (LCM) of 199 and 170
The least common multiple (LCM) of 199 and 170 is 33830.
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 199 and 170?
First, calculate the GCD of 199 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 170 = 1 remainder 29 |
| 2 | 170 ÷ 29 = 5 remainder 25 |
| 3 | 29 ÷ 25 = 1 remainder 4 |
| 4 | 25 ÷ 4 = 6 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 105 | 1995 |
| 14 and 45 | 630 |
| 196 and 144 | 7056 |
| 163 and 115 | 18745 |
| 47 and 181 | 8507 |