Least Common Multiple (LCM) of 131 and 75
The least common multiple (LCM) of 131 and 75 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 131 and 75?
First, calculate the GCD of 131 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 75 = 1 remainder 56 |
| 2 | 75 ÷ 56 = 1 remainder 19 |
| 3 | 56 ÷ 19 = 2 remainder 18 |
| 4 | 19 ÷ 18 = 1 remainder 1 |
| 5 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 47 | 1739 |
| 177 and 161 | 28497 |
| 114 and 62 | 3534 |
| 54 and 37 | 1998 |
| 135 and 55 | 1485 |