Least Common Multiple (LCM) of 130 and 185
The least common multiple (LCM) of 130 and 185 is 4810.
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 185?
First, calculate the GCD of 130 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 185 = 0 remainder 130 |
| 2 | 185 ÷ 130 = 1 remainder 55 |
| 3 | 130 ÷ 55 = 2 remainder 20 |
| 4 | 55 ÷ 20 = 2 remainder 15 |
| 5 | 20 ÷ 15 = 1 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 20 | 580 |
| 28 and 105 | 420 |
| 165 and 114 | 6270 |
| 103 and 54 | 5562 |
| 31 and 27 | 837 |