Least Common Multiple (LCM) of 185 and 96
The least common multiple (LCM) of 185 and 96 is 17760.
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 185 and 96?
First, calculate the GCD of 185 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 96 = 1 remainder 89 |
| 2 | 96 ÷ 89 = 1 remainder 7 |
| 3 | 89 ÷ 7 = 12 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 144 | 1872 |
| 135 and 80 | 2160 |
| 56 and 129 | 7224 |
| 105 and 14 | 210 |
| 183 and 95 | 17385 |