Least Common Multiple (LCM) of 33 and 89
The least common multiple (LCM) of 33 and 89 is 2937.
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 89?
First, calculate the GCD of 33 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 89 = 0 remainder 33 |
| 2 | 89 ÷ 33 = 2 remainder 23 |
| 3 | 33 ÷ 23 = 1 remainder 10 |
| 4 | 23 ÷ 10 = 2 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 20 | 3460 |
| 197 and 198 | 39006 |
| 193 and 144 | 27792 |
| 138 and 125 | 17250 |
| 42 and 14 | 42 |