Least Common Multiple (LCM) of 109 and 33
The least common multiple (LCM) of 109 and 33 is 3597.
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 109 and 33?
First, calculate the GCD of 109 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 33 = 3 remainder 10 |
| 2 | 33 ÷ 10 = 3 remainder 3 |
| 3 | 10 ÷ 3 = 3 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 57 | 9804 |
| 45 and 66 | 990 |
| 162 and 165 | 8910 |
| 125 and 103 | 12875 |
| 55 and 65 | 715 |