Least Common Multiple (LCM) of 33 and 185
The least common multiple (LCM) of 33 and 185 is 6105.
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 185?
First, calculate the GCD of 33 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 185 = 0 remainder 33 |
| 2 | 185 ÷ 33 = 5 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 |
|---|---|
| 172 and 55 | 9460 |
| 80 and 151 | 12080 |
| 78 and 130 | 390 |
| 188 and 42 | 3948 |
| 135 and 197 | 26595 |