Least Common Multiple (LCM) of 54 and 114
The least common multiple (LCM) of 54 and 114 is 1026.
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 114?
First, calculate the GCD of 54 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 114 = 0 remainder 54 |
| 2 | 114 ÷ 54 = 2 remainder 6 |
| 3 | 54 ÷ 6 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 183 | 11529 |
| 197 and 31 | 6107 |
| 117 and 85 | 9945 |
| 44 and 146 | 3212 |
| 38 and 84 | 1596 |