Least Common Multiple (LCM) of 111 and 128
The least common multiple (LCM) of 111 and 128 is 14208.
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 111 and 128?
First, calculate the GCD of 111 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 128 = 0 remainder 111 |
| 2 | 128 ÷ 111 = 1 remainder 17 |
| 3 | 111 ÷ 17 = 6 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 47 | 3901 |
| 17 and 91 | 1547 |
| 102 and 140 | 7140 |
| 93 and 148 | 13764 |
| 199 and 11 | 2189 |