Least Common Multiple (LCM) of 54 and 40
The least common multiple (LCM) of 54 and 40 is 1080.
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 40?
First, calculate the GCD of 54 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 40 = 1 remainder 14 |
| 2 | 40 ÷ 14 = 2 remainder 12 |
| 3 | 14 ÷ 12 = 1 remainder 2 |
| 4 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 175 | 175 |
| 138 and 37 | 5106 |
| 105 and 107 | 11235 |
| 134 and 53 | 7102 |
| 113 and 147 | 16611 |