Least Common Multiple (LCM) of 75 and 39
The least common multiple (LCM) of 75 and 39 is 975.
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 39?
First, calculate the GCD of 75 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 39 = 1 remainder 36 |
| 2 | 39 ÷ 36 = 1 remainder 3 |
| 3 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 135 | 17280 |
| 14 and 133 | 266 |
| 173 and 96 | 16608 |
| 162 and 58 | 4698 |
| 89 and 20 | 1780 |