Least Common Multiple (LCM) of 44 and 54
The least common multiple (LCM) of 44 and 54 is 1188.
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 44 and 54?
First, calculate the GCD of 44 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 44 ÷ 54 = 0 remainder 44 |
| 2 | 54 ÷ 44 = 1 remainder 10 |
| 3 | 44 ÷ 10 = 4 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 200 | 200 |
| 162 and 12 | 324 |
| 100 and 126 | 6300 |
| 111 and 28 | 3108 |
| 117 and 90 | 1170 |