Least Common Multiple (LCM) of 105 and 33
The least common multiple (LCM) of 105 and 33 is 1155.
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 105 and 33?
First, calculate the GCD of 105 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 33 = 3 remainder 6 |
| 2 | 33 ÷ 6 = 5 remainder 3 |
| 3 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 127 | 25146 |
| 166 and 99 | 16434 |
| 180 and 198 | 1980 |
| 160 and 104 | 2080 |
| 42 and 23 | 966 |