Least Common Multiple (LCM) of 17 and 33
The least common multiple (LCM) of 17 and 33 is 561.
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 17 and 33?
First, calculate the GCD of 17 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 33 = 0 remainder 17 |
| 2 | 33 ÷ 17 = 1 remainder 16 |
| 3 | 17 ÷ 16 = 1 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 97 | 14162 |
| 70 and 150 | 1050 |
| 65 and 121 | 7865 |
| 175 and 20 | 700 |
| 112 and 87 | 9744 |