Least Common Multiple (LCM) of 104 and 194
The least common multiple (LCM) of 104 and 194 is 10088.
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 194?
First, calculate the GCD of 104 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 194 = 0 remainder 104 |
| 2 | 194 ÷ 104 = 1 remainder 90 |
| 3 | 104 ÷ 90 = 1 remainder 14 |
| 4 | 90 ÷ 14 = 6 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 29 | 2088 |
| 51 and 154 | 7854 |
| 112 and 119 | 1904 |
| 194 and 197 | 38218 |
| 19 and 188 | 3572 |