Least Common Multiple (LCM) of 43 and 54
The least common multiple (LCM) of 43 and 54 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 43 and 54?
First, calculate the GCD of 43 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 54 = 0 remainder 43 |
| 2 | 54 ÷ 43 = 1 remainder 11 |
| 3 | 43 ÷ 11 = 3 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 70 | 1260 |
| 27 and 187 | 5049 |
| 53 and 172 | 9116 |
| 63 and 172 | 10836 |
| 65 and 67 | 4355 |