Least Common Multiple (LCM) of 81 and 103
The least common multiple (LCM) of 81 and 103 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 81 and 103?
First, calculate the GCD of 81 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 103 = 0 remainder 81 |
| 2 | 103 ÷ 81 = 1 remainder 22 |
| 3 | 81 ÷ 22 = 3 remainder 15 |
| 4 | 22 ÷ 15 = 1 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 92 | 10396 |
| 146 and 104 | 7592 |
| 184 and 70 | 6440 |
| 73 and 47 | 3431 |
| 90 and 102 | 1530 |