Least Common Multiple (LCM) of 104 and 199
The least common multiple (LCM) of 104 and 199 is 20696.
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 199?
First, calculate the GCD of 104 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 199 = 0 remainder 104 |
| 2 | 199 ÷ 104 = 1 remainder 95 |
| 3 | 104 ÷ 95 = 1 remainder 9 |
| 4 | 95 ÷ 9 = 10 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 28 | 420 |
| 98 and 157 | 15386 |
| 14 and 185 | 2590 |
| 15 and 12 | 60 |
| 15 and 107 | 1605 |