Least Common Multiple (LCM) of 24 and 96
The least common multiple (LCM) of 24 and 96 is 96.
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 96?
First, calculate the GCD of 24 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 96 = 0 remainder 24 |
| 2 | 96 ÷ 24 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 160 | 800 |
| 74 and 82 | 3034 |
| 99 and 78 | 2574 |
| 75 and 99 | 2475 |
| 199 and 109 | 21691 |