Least Common Multiple (LCM) of 27 and 104
The least common multiple (LCM) of 27 and 104 is 2808.
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 104?
First, calculate the GCD of 27 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 104 = 0 remainder 27 |
| 2 | 104 ÷ 27 = 3 remainder 23 |
| 3 | 27 ÷ 23 = 1 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 52 | 5980 |
| 116 and 123 | 14268 |
| 132 and 56 | 1848 |
| 137 and 101 | 13837 |
| 82 and 27 | 2214 |