Least Common Multiple (LCM) of 54 and 144
The least common multiple (LCM) of 54 and 144 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 144?
First, calculate the GCD of 54 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 144 = 0 remainder 54 |
| 2 | 144 ÷ 54 = 2 remainder 36 |
| 3 | 54 ÷ 36 = 1 remainder 18 |
| 4 | 36 ÷ 18 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 14 | 84 |
| 50 and 143 | 7150 |
| 57 and 105 | 1995 |
| 164 and 190 | 15580 |
| 127 and 114 | 14478 |