Least Common Multiple (LCM) of 96 and 131
The least common multiple (LCM) of 96 and 131 is 12576.
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 131?
First, calculate the GCD of 96 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 131 = 0 remainder 96 |
| 2 | 131 ÷ 96 = 1 remainder 35 |
| 3 | 96 ÷ 35 = 2 remainder 26 |
| 4 | 35 ÷ 26 = 1 remainder 9 |
| 5 | 26 ÷ 9 = 2 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 114 | 3990 |
| 83 and 19 | 1577 |
| 40 and 114 | 2280 |
| 198 and 176 | 1584 |
| 146 and 17 | 2482 |