Least Common Multiple (LCM) of 104 and 185
The least common multiple (LCM) of 104 and 185 is 19240.
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 104 and 185?
First, calculate the GCD of 104 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 185 = 0 remainder 104 |
| 2 | 185 ÷ 104 = 1 remainder 81 |
| 3 | 104 ÷ 81 = 1 remainder 23 |
| 4 | 81 ÷ 23 = 3 remainder 12 |
| 5 | 23 ÷ 12 = 1 remainder 11 |
| 6 | 12 ÷ 11 = 1 remainder 1 |
| 7 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 125 | 3875 |
| 110 and 171 | 18810 |
| 200 and 193 | 38600 |
| 147 and 33 | 1617 |
| 85 and 181 | 15385 |