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 |
|---|---|
| 181 and 143 | 25883 |
| 170 and 173 | 29410 |
| 112 and 79 | 8848 |
| 194 and 57 | 11058 |
| 180 and 188 | 8460 |