Least Common Multiple (LCM) of 78 and 96
The least common multiple (LCM) of 78 and 96 is 1248.
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 78 and 96?
First, calculate the GCD of 78 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 96 = 0 remainder 78 |
| 2 | 96 ÷ 78 = 1 remainder 18 |
| 3 | 78 ÷ 18 = 4 remainder 6 |
| 4 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 42 | 2562 |
| 177 and 129 | 7611 |
| 114 and 89 | 10146 |
| 55 and 96 | 5280 |
| 101 and 83 | 8383 |