Least Common Multiple (LCM) of 54 and 178
The least common multiple (LCM) of 54 and 178 is 4806.
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 178?
First, calculate the GCD of 54 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 178 = 0 remainder 54 |
| 2 | 178 ÷ 54 = 3 remainder 16 |
| 3 | 54 ÷ 16 = 3 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 141 | 20586 |
| 75 and 27 | 675 |
| 172 and 60 | 2580 |
| 186 and 119 | 22134 |
| 66 and 48 | 528 |