Least Common Multiple (LCM) of 185 and 104
The least common multiple (LCM) of 185 and 104 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 185 and 104?
First, calculate the GCD of 185 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 104 = 1 remainder 81 |
| 2 | 104 ÷ 81 = 1 remainder 23 |
| 3 | 81 ÷ 23 = 3 remainder 12 |
| 4 | 23 ÷ 12 = 1 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 50 | 1550 |
| 24 and 172 | 1032 |
| 189 and 141 | 8883 |
| 91 and 140 | 1820 |
| 199 and 156 | 31044 |