Least Common Multiple (LCM) of 33 and 86
The least common multiple (LCM) of 33 and 86 is 2838.
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 86?
First, calculate the GCD of 33 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 86 = 0 remainder 33 |
| 2 | 86 ÷ 33 = 2 remainder 20 |
| 3 | 33 ÷ 20 = 1 remainder 13 |
| 4 | 20 ÷ 13 = 1 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 46 | 4140 |
| 74 and 65 | 4810 |
| 196 and 31 | 6076 |
| 143 and 199 | 28457 |
| 135 and 103 | 13905 |