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 |
|---|---|
| 180 and 197 | 35460 |
| 193 and 194 | 37442 |
| 78 and 66 | 858 |
| 152 and 92 | 3496 |
| 14 and 132 | 924 |