Least Common Multiple (LCM) of 27 and 111
The least common multiple (LCM) of 27 and 111 is 999.
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 27 and 111?
First, calculate the GCD of 27 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 111 = 0 remainder 27 |
| 2 | 111 ÷ 27 = 4 remainder 3 |
| 3 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 171 | 9918 |
| 45 and 121 | 5445 |
| 88 and 74 | 3256 |
| 54 and 63 | 378 |
| 34 and 178 | 3026 |