Least Common Multiple (LCM) of 170 and 199
The least common multiple (LCM) of 170 and 199 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 170 and 199?
First, calculate the GCD of 170 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 199 = 0 remainder 170 |
| 2 | 199 ÷ 170 = 1 remainder 29 |
| 3 | 170 ÷ 29 = 5 remainder 25 |
| 4 | 29 ÷ 25 = 1 remainder 4 |
| 5 | 25 ÷ 4 = 6 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 134 | 2278 |
| 82 and 120 | 4920 |
| 190 and 128 | 12160 |
| 15 and 80 | 240 |
| 49 and 72 | 3528 |