Least Common Multiple (LCM) of 103 and 81
The least common multiple (LCM) of 103 and 81 is 8343.
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 81?
First, calculate the GCD of 103 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 81 = 1 remainder 22 |
| 2 | 81 ÷ 22 = 3 remainder 15 |
| 3 | 22 ÷ 15 = 1 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 183 | 11895 |
| 98 and 190 | 9310 |
| 108 and 144 | 432 |
| 59 and 166 | 9794 |
| 51 and 38 | 1938 |