Least Common Multiple (LCM) of 130 and 96
The least common multiple (LCM) of 130 and 96 is 6240.
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 96?
First, calculate the GCD of 130 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 96 = 1 remainder 34 |
| 2 | 96 ÷ 34 = 2 remainder 28 |
| 3 | 34 ÷ 28 = 1 remainder 6 |
| 4 | 28 ÷ 6 = 4 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 69 | 828 |
| 177 and 139 | 24603 |
| 19 and 76 | 76 |
| 54 and 10 | 270 |
| 87 and 188 | 16356 |