Least Common Multiple (LCM) of 75 and 108
The least common multiple (LCM) of 75 and 108 is 2700.
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 108?
First, calculate the GCD of 75 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 108 = 0 remainder 75 |
| 2 | 108 ÷ 75 = 1 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 |
|---|---|
| 151 and 37 | 5587 |
| 165 and 80 | 2640 |
| 90 and 155 | 2790 |
| 150 and 175 | 1050 |
| 193 and 131 | 25283 |