Least Common Multiple (LCM) of 54 and 104
The least common multiple (LCM) of 54 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 54 and 104?
First, calculate the GCD of 54 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 104 = 0 remainder 54 |
| 2 | 104 ÷ 54 = 1 remainder 50 |
| 3 | 54 ÷ 50 = 1 remainder 4 |
| 4 | 50 ÷ 4 = 12 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 22 | 1474 |
| 65 and 157 | 10205 |
| 196 and 16 | 784 |
| 159 and 97 | 15423 |
| 186 and 163 | 30318 |