Least Common Multiple (LCM) of 17 and 65
The least common multiple (LCM) of 17 and 65 is 1105.
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 65?
First, calculate the GCD of 17 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 65 = 0 remainder 17 |
| 2 | 65 ÷ 17 = 3 remainder 14 |
| 3 | 17 ÷ 14 = 1 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 166 | 8798 |
| 115 and 179 | 20585 |
| 114 and 174 | 3306 |
| 45 and 141 | 2115 |
| 185 and 73 | 13505 |