Least Common Multiple (LCM) of 130 and 38
The least common multiple (LCM) of 130 and 38 is 2470.
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 38?
First, calculate the GCD of 130 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 38 = 3 remainder 16 |
| 2 | 38 ÷ 16 = 2 remainder 6 |
| 3 | 16 ÷ 6 = 2 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 128 | 17536 |
| 114 and 39 | 1482 |
| 139 and 62 | 8618 |
| 115 and 170 | 3910 |
| 137 and 142 | 19454 |