Least Common Multiple (LCM) of 65 and 17
The least common multiple (LCM) of 65 and 17 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 65 and 17?
First, calculate the GCD of 65 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 17 = 3 remainder 14 |
| 2 | 17 ÷ 14 = 1 remainder 3 |
| 3 | 14 ÷ 3 = 4 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 165 | 21615 |
| 41 and 103 | 4223 |
| 160 and 176 | 1760 |
| 80 and 192 | 960 |
| 167 and 32 | 5344 |