Least Common Multiple (LCM) of 75 and 135
The least common multiple (LCM) of 75 and 135 is 675.
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 135?
First, calculate the GCD of 75 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 135 = 0 remainder 75 |
| 2 | 135 ÷ 75 = 1 remainder 60 |
| 3 | 75 ÷ 60 = 1 remainder 15 |
| 4 | 60 ÷ 15 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 11 | 2046 |
| 188 and 154 | 14476 |
| 77 and 14 | 154 |
| 136 and 110 | 7480 |
| 24 and 57 | 456 |