Least Common Multiple (LCM) of 75 and 32
The least common multiple (LCM) of 75 and 32 is 2400.
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 32?
First, calculate the GCD of 75 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 32 = 2 remainder 11 |
| 2 | 32 ÷ 11 = 2 remainder 10 |
| 3 | 11 ÷ 10 = 1 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 176 | 16368 |
| 51 and 35 | 1785 |
| 144 and 72 | 144 |
| 86 and 17 | 1462 |
| 115 and 82 | 9430 |