Least Common Multiple (LCM) of 33 and 19
The least common multiple (LCM) of 33 and 19 is 627.
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 19?
First, calculate the GCD of 33 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 19 = 1 remainder 14 |
| 2 | 19 ÷ 14 = 1 remainder 5 |
| 3 | 14 ÷ 5 = 2 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 127 | 13081 |
| 74 and 176 | 6512 |
| 24 and 100 | 600 |
| 30 and 175 | 1050 |
| 81 and 154 | 12474 |