Least Common Multiple (LCM) of 75 and 131
The least common multiple (LCM) of 75 and 131 is 9825.
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 75 and 131?
First, calculate the GCD of 75 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 131 = 0 remainder 75 |
| 2 | 131 ÷ 75 = 1 remainder 56 |
| 3 | 75 ÷ 56 = 1 remainder 19 |
| 4 | 56 ÷ 19 = 2 remainder 18 |
| 5 | 19 ÷ 18 = 1 remainder 1 |
| 6 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 142 | 6816 |
| 67 and 95 | 6365 |
| 111 and 184 | 20424 |
| 115 and 105 | 2415 |
| 149 and 14 | 2086 |