Least Common Multiple (LCM) of 103 and 197
The least common multiple (LCM) of 103 and 197 is 20291.
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 197?
First, calculate the GCD of 103 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 197 = 0 remainder 103 |
| 2 | 197 ÷ 103 = 1 remainder 94 |
| 3 | 103 ÷ 94 = 1 remainder 9 |
| 4 | 94 ÷ 9 = 10 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 131 | 14410 |
| 103 and 119 | 12257 |
| 126 and 125 | 15750 |
| 144 and 10 | 720 |
| 176 and 140 | 6160 |