Least Common Multiple (LCM) of 130 and 47
The least common multiple (LCM) of 130 and 47 is 6110.
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 47?
First, calculate the GCD of 130 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 47 = 2 remainder 36 |
| 2 | 47 ÷ 36 = 1 remainder 11 |
| 3 | 36 ÷ 11 = 3 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 67 | 6365 |
| 38 and 66 | 1254 |
| 165 and 180 | 1980 |
| 169 and 168 | 28392 |
| 134 and 23 | 3082 |