Least Common Multiple (LCM) of 111 and 65
The least common multiple (LCM) of 111 and 65 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 111 and 65?
First, calculate the GCD of 111 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 65 = 1 remainder 46 |
| 2 | 65 ÷ 46 = 1 remainder 19 |
| 3 | 46 ÷ 19 = 2 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 126 | 126 |
| 69 and 79 | 5451 |
| 42 and 198 | 1386 |
| 195 and 169 | 2535 |
| 178 and 137 | 24386 |