Least Common Multiple (LCM) of 96 and 38
The least common multiple (LCM) of 96 and 38 is 1824.
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 96 and 38?
First, calculate the GCD of 96 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 38 = 2 remainder 20 |
| 2 | 38 ÷ 20 = 1 remainder 18 |
| 3 | 20 ÷ 18 = 1 remainder 2 |
| 4 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 101 | 4545 |
| 195 and 42 | 2730 |
| 82 and 125 | 10250 |
| 20 and 50 | 100 |
| 66 and 49 | 3234 |