Least Common Multiple (LCM) of 103 and 200
The least common multiple (LCM) of 103 and 200 is 20600.
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 200?
First, calculate the GCD of 103 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 200 = 0 remainder 103 |
| 2 | 200 ÷ 103 = 1 remainder 97 |
| 3 | 103 ÷ 97 = 1 remainder 6 |
| 4 | 97 ÷ 6 = 16 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 162 | 5022 |
| 54 and 30 | 270 |
| 174 and 106 | 9222 |
| 73 and 195 | 14235 |
| 122 and 45 | 5490 |