Least Common Multiple (LCM) of 43 and 192
The least common multiple (LCM) of 43 and 192 is 8256.
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 192?
First, calculate the GCD of 43 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 192 = 0 remainder 43 |
| 2 | 192 ÷ 43 = 4 remainder 20 |
| 3 | 43 ÷ 20 = 2 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 88 | 3784 |
| 144 and 64 | 576 |
| 114 and 36 | 684 |
| 116 and 100 | 2900 |
| 184 and 144 | 3312 |