Least Common Multiple (LCM) of 189 and 33
The least common multiple (LCM) of 189 and 33 is 2079.
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 189 and 33?
First, calculate the GCD of 189 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 33 = 5 remainder 24 |
| 2 | 33 ÷ 24 = 1 remainder 9 |
| 3 | 24 ÷ 9 = 2 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 195 | 17160 |
| 31 and 184 | 5704 |
| 133 and 59 | 7847 |
| 93 and 96 | 2976 |
| 163 and 84 | 13692 |