Least Common Multiple (LCM) of 33 and 85
The least common multiple (LCM) of 33 and 85 is 2805.
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 33 and 85?
First, calculate the GCD of 33 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 85 = 0 remainder 33 |
| 2 | 85 ÷ 33 = 2 remainder 19 |
| 3 | 33 ÷ 19 = 1 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 89 | 4361 |
| 128 and 159 | 20352 |
| 120 and 51 | 2040 |
| 104 and 149 | 15496 |
| 180 and 82 | 7380 |