Least Common Multiple (LCM) of 96 and 130
The least common multiple (LCM) of 96 and 130 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 96 and 130?
First, calculate the GCD of 96 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 130 = 0 remainder 96 |
| 2 | 130 ÷ 96 = 1 remainder 34 |
| 3 | 96 ÷ 34 = 2 remainder 28 |
| 4 | 34 ÷ 28 = 1 remainder 6 |
| 5 | 28 ÷ 6 = 4 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 150 | 2100 |
| 188 and 49 | 9212 |
| 166 and 195 | 32370 |
| 129 and 33 | 1419 |
| 99 and 135 | 1485 |