Least Common Multiple (LCM) of 199 and 104
The least common multiple (LCM) of 199 and 104 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 199 and 104?
First, calculate the GCD of 199 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 104 = 1 remainder 95 |
| 2 | 104 ÷ 95 = 1 remainder 9 |
| 3 | 95 ÷ 9 = 10 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 50 | 1650 |
| 118 and 43 | 5074 |
| 197 and 57 | 11229 |
| 64 and 189 | 12096 |
| 116 and 134 | 7772 |