Least Common Multiple (LCM) of 197 and 103
The least common multiple (LCM) of 197 and 103 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 197 and 103?
First, calculate the GCD of 197 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 103 = 1 remainder 94 |
| 2 | 103 ÷ 94 = 1 remainder 9 |
| 3 | 94 ÷ 9 = 10 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 89 | 7031 |
| 81 and 12 | 324 |
| 88 and 49 | 4312 |
| 33 and 171 | 1881 |
| 114 and 172 | 9804 |