Least Common Multiple (LCM) of 130 and 48
The least common multiple (LCM) of 130 and 48 is 3120.
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 48?
First, calculate the GCD of 130 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 48 = 2 remainder 34 |
| 2 | 48 ÷ 34 = 1 remainder 14 |
| 3 | 34 ÷ 14 = 2 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 55 | 9405 |
| 199 and 47 | 9353 |
| 156 and 73 | 11388 |
| 168 and 109 | 18312 |
| 16 and 53 | 848 |