Least Common Multiple (LCM) of 88 and 111
The least common multiple (LCM) of 88 and 111 is 9768.
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 88 and 111?
First, calculate the GCD of 88 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 88 ÷ 111 = 0 remainder 88 |
| 2 | 111 ÷ 88 = 1 remainder 23 |
| 3 | 88 ÷ 23 = 3 remainder 19 |
| 4 | 23 ÷ 19 = 1 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 82 | 11726 |
| 75 and 139 | 10425 |
| 32 and 105 | 3360 |
| 128 and 199 | 25472 |
| 10 and 195 | 390 |