Least Common Multiple (LCM) of 54 and 48
The least common multiple (LCM) of 54 and 48 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 54 and 48?
First, calculate the GCD of 54 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 48 = 1 remainder 6 |
| 2 | 48 ÷ 6 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 142 | 7526 |
| 144 and 90 | 720 |
| 178 and 112 | 9968 |
| 170 and 55 | 1870 |
| 55 and 12 | 660 |