Least Common Multiple (LCM) of 130 and 103
The least common multiple (LCM) of 130 and 103 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 130 and 103?
First, calculate the GCD of 130 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 103 = 1 remainder 27 |
| 2 | 103 ÷ 27 = 3 remainder 22 |
| 3 | 27 ÷ 22 = 1 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 155 | 15965 |
| 189 and 161 | 4347 |
| 162 and 184 | 14904 |
| 190 and 41 | 7790 |
| 43 and 178 | 7654 |