Least Common Multiple (LCM) of 20 and 54
The least common multiple (LCM) of 20 and 54 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 20 and 54?
First, calculate the GCD of 20 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 54 = 0 remainder 20 |
| 2 | 54 ÷ 20 = 2 remainder 14 |
| 3 | 20 ÷ 14 = 1 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 152 | 26904 |
| 122 and 39 | 4758 |
| 104 and 61 | 6344 |
| 92 and 197 | 18124 |
| 70 and 132 | 4620 |