Least Common Multiple (LCM) of 85 and 96
The least common multiple (LCM) of 85 and 96 is 8160.
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 85 and 96?
First, calculate the GCD of 85 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 96 = 0 remainder 85 |
| 2 | 96 ÷ 85 = 1 remainder 11 |
| 3 | 85 ÷ 11 = 7 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 199 | 36815 |
| 63 and 107 | 6741 |
| 64 and 74 | 2368 |
| 149 and 36 | 5364 |
| 55 and 12 | 660 |