Least Common Multiple (LCM) of 19 and 33
The least common multiple (LCM) of 19 and 33 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 19 and 33?
First, calculate the GCD of 19 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 33 = 0 remainder 19 |
| 2 | 33 ÷ 19 = 1 remainder 14 |
| 3 | 19 ÷ 14 = 1 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 110 | 770 |
| 139 and 127 | 17653 |
| 85 and 122 | 10370 |
| 12 and 131 | 1572 |
| 56 and 173 | 9688 |