Least Common Multiple (LCM) of 24 and 75
The least common multiple (LCM) of 24 and 75 is 600.
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 24 and 75?
First, calculate the GCD of 24 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 75 = 0 remainder 24 |
| 2 | 75 ÷ 24 = 3 remainder 3 |
| 3 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 51 | 2397 |
| 31 and 26 | 806 |
| 184 and 87 | 16008 |
| 184 and 31 | 5704 |
| 19 and 193 | 3667 |