Least Common Multiple (LCM) of 54 and 56
The least common multiple (LCM) of 54 and 56 is 1512.
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 56?
First, calculate the GCD of 54 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 56 = 0 remainder 54 |
| 2 | 56 ÷ 54 = 1 remainder 2 |
| 3 | 54 ÷ 2 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 95 | 3325 |
| 101 and 151 | 15251 |
| 105 and 15 | 105 |
| 125 and 23 | 2875 |
| 14 and 19 | 266 |