Least Common Multiple (LCM) of 65 and 111
The least common multiple (LCM) of 65 and 111 is 7215.
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 111?
First, calculate the GCD of 65 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 111 = 0 remainder 65 |
| 2 | 111 ÷ 65 = 1 remainder 46 |
| 3 | 65 ÷ 46 = 1 remainder 19 |
| 4 | 46 ÷ 19 = 2 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 114 | 6270 |
| 21 and 156 | 1092 |
| 28 and 84 | 84 |
| 24 and 154 | 1848 |
| 142 and 65 | 9230 |