Least Common Multiple (LCM) of 48 and 54
The least common multiple (LCM) of 48 and 54 is 432.
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 48 and 54?
First, calculate the GCD of 48 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 54 = 0 remainder 48 |
| 2 | 54 ÷ 48 = 1 remainder 6 |
| 3 | 48 ÷ 6 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 169 | 17914 |
| 25 and 125 | 125 |
| 26 and 133 | 3458 |
| 83 and 186 | 15438 |
| 45 and 177 | 2655 |