Least Common Multiple (LCM) of 109 and 96
The least common multiple (LCM) of 109 and 96 is 10464.
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 109 and 96?
First, calculate the GCD of 109 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 96 = 1 remainder 13 |
| 2 | 96 ÷ 13 = 7 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 71 | 1988 |
| 85 and 83 | 7055 |
| 198 and 132 | 396 |
| 71 and 21 | 1491 |
| 89 and 173 | 15397 |