Least Common Multiple (LCM) of 131 and 96
The least common multiple (LCM) of 131 and 96 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 131 and 96?
First, calculate the GCD of 131 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 96 = 1 remainder 35 |
| 2 | 96 ÷ 35 = 2 remainder 26 |
| 3 | 35 ÷ 26 = 1 remainder 9 |
| 4 | 26 ÷ 9 = 2 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 16 | 1392 |
| 55 and 13 | 715 |
| 31 and 136 | 4216 |
| 174 and 123 | 7134 |
| 176 and 32 | 352 |