Least Common Multiple (LCM) of 17 and 32
The least common multiple (LCM) of 17 and 32 is 544.
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 32?
First, calculate the GCD of 17 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 32 = 0 remainder 17 |
| 2 | 32 ÷ 17 = 1 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 101 | 6161 |
| 164 and 67 | 10988 |
| 11 and 36 | 396 |
| 84 and 98 | 588 |
| 148 and 168 | 6216 |