Least Common Multiple (LCM) of 199 and 85
The least common multiple (LCM) of 199 and 85 is 16915.
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 85?
First, calculate the GCD of 199 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 85 = 2 remainder 29 |
| 2 | 85 ÷ 29 = 2 remainder 27 |
| 3 | 29 ÷ 27 = 1 remainder 2 |
| 4 | 27 ÷ 2 = 13 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 123 | 5781 |
| 54 and 103 | 5562 |
| 33 and 14 | 462 |
| 23 and 99 | 2277 |
| 67 and 79 | 5293 |