Least Common Multiple (LCM) of 43 and 188
The least common multiple (LCM) of 43 and 188 is 8084.
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 188?
First, calculate the GCD of 43 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 188 = 0 remainder 43 |
| 2 | 188 ÷ 43 = 4 remainder 16 |
| 3 | 43 ÷ 16 = 2 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 190 | 3990 |
| 28 and 95 | 2660 |
| 79 and 114 | 9006 |
| 14 and 200 | 1400 |
| 174 and 134 | 11658 |