Least Common Multiple (LCM) of 43 and 111
The least common multiple (LCM) of 43 and 111 is 4773.
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 111?
First, calculate the GCD of 43 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 111 = 0 remainder 43 |
| 2 | 111 ÷ 43 = 2 remainder 25 |
| 3 | 43 ÷ 25 = 1 remainder 18 |
| 4 | 25 ÷ 18 = 1 remainder 7 |
| 5 | 18 ÷ 7 = 2 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 147 | 7350 |
| 178 and 46 | 4094 |
| 197 and 18 | 3546 |
| 101 and 40 | 4040 |
| 59 and 41 | 2419 |