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 |
|---|---|
| 122 and 136 | 8296 |
| 142 and 163 | 23146 |
| 184 and 59 | 10856 |
| 109 and 31 | 3379 |
| 158 and 113 | 17854 |