Least Common Multiple (LCM) of 12 and 33
The least common multiple (LCM) of 12 and 33 is 132.
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 12 and 33?
First, calculate the GCD of 12 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 33 = 0 remainder 12 |
| 2 | 33 ÷ 12 = 2 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 68 | 4692 |
| 167 and 183 | 30561 |
| 23 and 36 | 828 |
| 60 and 97 | 5820 |
| 144 and 123 | 5904 |