Least Common Multiple (LCM) of 75 and 183
The least common multiple (LCM) of 75 and 183 is 4575.
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 183?
First, calculate the GCD of 75 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 183 = 0 remainder 75 |
| 2 | 183 ÷ 75 = 2 remainder 33 |
| 3 | 75 ÷ 33 = 2 remainder 9 |
| 4 | 33 ÷ 9 = 3 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 22 | 682 |
| 17 and 11 | 187 |
| 58 and 111 | 6438 |
| 97 and 65 | 6305 |
| 120 and 118 | 7080 |