Least Common Multiple (LCM) of 185 and 199
The least common multiple (LCM) of 185 and 199 is 36815.
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 185 and 199?
First, calculate the GCD of 185 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 199 = 0 remainder 185 |
| 2 | 199 ÷ 185 = 1 remainder 14 |
| 3 | 185 ÷ 14 = 13 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 151 | 14647 |
| 49 and 42 | 294 |
| 199 and 33 | 6567 |
| 98 and 114 | 5586 |
| 13 and 63 | 819 |