Least Common Multiple (LCM) of 17 and 27
The least common multiple (LCM) of 17 and 27 is 459.
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 27?
First, calculate the GCD of 17 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 27 = 0 remainder 17 |
| 2 | 27 ÷ 17 = 1 remainder 10 |
| 3 | 17 ÷ 10 = 1 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 46 | 5658 |
| 96 and 105 | 3360 |
| 31 and 68 | 2108 |
| 177 and 112 | 19824 |
| 194 and 144 | 13968 |