Least Common Multiple (LCM) of 96 and 109
The least common multiple (LCM) of 96 and 109 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 96 and 109?
First, calculate the GCD of 96 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 109 = 0 remainder 96 |
| 2 | 109 ÷ 96 = 1 remainder 13 |
| 3 | 96 ÷ 13 = 7 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 19 | 2090 |
| 94 and 55 | 5170 |
| 148 and 178 | 13172 |
| 175 and 53 | 9275 |
| 80 and 14 | 560 |