Least Common Multiple (LCM) of 103 and 130
The least common multiple (LCM) of 103 and 130 is 13390.
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 130?
First, calculate the GCD of 103 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 130 = 0 remainder 103 |
| 2 | 130 ÷ 103 = 1 remainder 27 |
| 3 | 103 ÷ 27 = 3 remainder 22 |
| 4 | 27 ÷ 22 = 1 remainder 5 |
| 5 | 22 ÷ 5 = 4 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 150 | 13350 |
| 65 and 105 | 1365 |
| 193 and 41 | 7913 |
| 137 and 166 | 22742 |
| 25 and 197 | 4925 |