Least Common Multiple (LCM) of 103 and 199
The least common multiple (LCM) of 103 and 199 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 103 and 199?
First, calculate the GCD of 103 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 199 = 0 remainder 103 |
| 2 | 199 ÷ 103 = 1 remainder 96 |
| 3 | 103 ÷ 96 = 1 remainder 7 |
| 4 | 96 ÷ 7 = 13 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 21 | 1218 |
| 82 and 97 | 7954 |
| 111 and 82 | 9102 |
| 64 and 161 | 10304 |
| 84 and 182 | 1092 |