Least Common Multiple (LCM) of 54 and 183
The least common multiple (LCM) of 54 and 183 is 3294.
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 183?
First, calculate the GCD of 54 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 183 = 0 remainder 54 |
| 2 | 183 ÷ 54 = 3 remainder 21 |
| 3 | 54 ÷ 21 = 2 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 189 | 10962 |
| 48 and 115 | 5520 |
| 21 and 42 | 42 |
| 175 and 55 | 1925 |
| 164 and 196 | 8036 |