Least Common Multiple (LCM) of 54 and 110
The least common multiple (LCM) of 54 and 110 is 2970.
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 110?
First, calculate the GCD of 54 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 110 = 0 remainder 54 |
| 2 | 110 ÷ 54 = 2 remainder 2 |
| 3 | 54 ÷ 2 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 66 | 1122 |
| 16 and 164 | 656 |
| 185 and 92 | 17020 |
| 145 and 138 | 20010 |
| 21 and 109 | 2289 |