Least Common Multiple (LCM) of 54 and 180
The least common multiple (LCM) of 54 and 180 is 540.
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 180?
First, calculate the GCD of 54 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 180 = 0 remainder 54 |
| 2 | 180 ÷ 54 = 3 remainder 18 |
| 3 | 54 ÷ 18 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 164 | 4592 |
| 105 and 74 | 7770 |
| 118 and 130 | 7670 |
| 60 and 200 | 600 |
| 147 and 23 | 3381 |