Least Common Multiple (LCM) of 103 and 97
The least common multiple (LCM) of 103 and 97 is 9991.
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 97?
First, calculate the GCD of 103 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 97 = 1 remainder 6 |
| 2 | 97 ÷ 6 = 16 remainder 1 |
| 3 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 90 | 270 |
| 190 and 159 | 30210 |
| 78 and 95 | 7410 |
| 135 and 141 | 6345 |
| 74 and 35 | 2590 |