Least Common Multiple (LCM) of 108 and 96
The least common multiple (LCM) of 108 and 96 is 864.
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 108 and 96?
First, calculate the GCD of 108 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 96 = 1 remainder 12 |
| 2 | 96 ÷ 12 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 57 | 2964 |
| 117 and 115 | 13455 |
| 77 and 90 | 6930 |
| 110 and 184 | 10120 |
| 116 and 107 | 12412 |