Least Common Multiple (LCM) of 96 and 185
The least common multiple (LCM) of 96 and 185 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 96 and 185?
First, calculate the GCD of 96 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 185 = 0 remainder 96 |
| 2 | 185 ÷ 96 = 1 remainder 89 |
| 3 | 96 ÷ 89 = 1 remainder 7 |
| 4 | 89 ÷ 7 = 12 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 92 | 8188 |
| 96 and 17 | 1632 |
| 45 and 34 | 1530 |
| 72 and 111 | 2664 |
| 132 and 64 | 2112 |