Least Common Multiple (LCM) of 43 and 108
The least common multiple (LCM) of 43 and 108 is 4644.
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 108?
First, calculate the GCD of 43 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 108 = 0 remainder 43 |
| 2 | 108 ÷ 43 = 2 remainder 22 |
| 3 | 43 ÷ 22 = 1 remainder 21 |
| 4 | 22 ÷ 21 = 1 remainder 1 |
| 5 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 118 | 8378 |
| 66 and 74 | 2442 |
| 135 and 183 | 8235 |
| 46 and 165 | 7590 |
| 111 and 63 | 2331 |