Least Common Multiple (LCM) of 54 and 43
The least common multiple (LCM) of 54 and 43 is 2322.
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 43?
First, calculate the GCD of 54 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 43 = 1 remainder 11 |
| 2 | 43 ÷ 11 = 3 remainder 10 |
| 3 | 11 ÷ 10 = 1 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 81 | 1782 |
| 112 and 125 | 14000 |
| 144 and 174 | 4176 |
| 69 and 131 | 9039 |
| 142 and 91 | 12922 |