Least Common Multiple (LCM) of 48 and 130
The least common multiple (LCM) of 48 and 130 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 48 and 130?
First, calculate the GCD of 48 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 130 = 0 remainder 48 |
| 2 | 130 ÷ 48 = 2 remainder 34 |
| 3 | 48 ÷ 34 = 1 remainder 14 |
| 4 | 34 ÷ 14 = 2 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 12 | 132 |
| 57 and 112 | 6384 |
| 71 and 77 | 5467 |
| 100 and 123 | 12300 |
| 114 and 165 | 6270 |