Least Common Multiple (LCM) of 75 and 28
The least common multiple (LCM) of 75 and 28 is 2100.
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 28?
First, calculate the GCD of 75 and 28 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 28 = 2 remainder 19 |
| 2 | 28 ÷ 19 = 1 remainder 9 |
| 3 | 19 ÷ 9 = 2 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 22 | 3190 |
| 96 and 142 | 6816 |
| 124 and 123 | 15252 |
| 84 and 166 | 6972 |
| 193 and 92 | 17756 |