Least Common Multiple (LCM) of 105 and 199
The least common multiple (LCM) of 105 and 199 is 20895.
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 105 and 199?
First, calculate the GCD of 105 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 199 = 0 remainder 105 |
| 2 | 199 ÷ 105 = 1 remainder 94 |
| 3 | 105 ÷ 94 = 1 remainder 11 |
| 4 | 94 ÷ 11 = 8 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 133 | 13699 |
| 153 and 72 | 1224 |
| 104 and 122 | 6344 |
| 28 and 122 | 1708 |
| 107 and 78 | 8346 |