Least Common Multiple (LCM) of 199 and 103
The least common multiple (LCM) of 199 and 103 is 20497.
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 103?
First, calculate the GCD of 199 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 103 = 1 remainder 96 |
| 2 | 103 ÷ 96 = 1 remainder 7 |
| 3 | 96 ÷ 7 = 13 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 124 | 5580 |
| 38 and 36 | 684 |
| 198 and 161 | 31878 |
| 165 and 32 | 5280 |
| 161 and 82 | 13202 |