Least Common Multiple (LCM) of 85 and 199
The least common multiple (LCM) of 85 and 199 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 85 and 199?
First, calculate the GCD of 85 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 199 = 0 remainder 85 |
| 2 | 199 ÷ 85 = 2 remainder 29 |
| 3 | 85 ÷ 29 = 2 remainder 27 |
| 4 | 29 ÷ 27 = 1 remainder 2 |
| 5 | 27 ÷ 2 = 13 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 33 | 528 |
| 80 and 60 | 240 |
| 111 and 180 | 6660 |
| 50 and 20 | 100 |
| 157 and 81 | 12717 |