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 |
|---|---|
| 137 and 153 | 20961 |
| 149 and 28 | 4172 |
| 123 and 127 | 15621 |
| 128 and 48 | 384 |
| 117 and 180 | 2340 |