Least Common Multiple (LCM) of 65 and 18
The least common multiple (LCM) of 65 and 18 is 1170.
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 18?
First, calculate the GCD of 65 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 18 = 3 remainder 11 |
| 2 | 18 ÷ 11 = 1 remainder 7 |
| 3 | 11 ÷ 7 = 1 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 65 | 1885 |
| 183 and 122 | 366 |
| 163 and 27 | 4401 |
| 34 and 191 | 6494 |
| 31 and 142 | 4402 |