Least Common Multiple (LCM) of 103 and 131
The least common multiple (LCM) of 103 and 131 is 13493.
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 131?
First, calculate the GCD of 103 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 131 = 0 remainder 103 |
| 2 | 131 ÷ 103 = 1 remainder 28 |
| 3 | 103 ÷ 28 = 3 remainder 19 |
| 4 | 28 ÷ 19 = 1 remainder 9 |
| 5 | 19 ÷ 9 = 2 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 155 | 10540 |
| 49 and 105 | 735 |
| 184 and 135 | 24840 |
| 162 and 16 | 1296 |
| 140 and 159 | 22260 |