Least Common Multiple (LCM) of 85 and 104
The least common multiple (LCM) of 85 and 104 is 8840.
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 104?
First, calculate the GCD of 85 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 104 = 0 remainder 85 |
| 2 | 104 ÷ 85 = 1 remainder 19 |
| 3 | 85 ÷ 19 = 4 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 89 | 10680 |
| 44 and 41 | 1804 |
| 108 and 14 | 756 |
| 14 and 183 | 2562 |
| 200 and 59 | 11800 |