Least Common Multiple (LCM) of 192 and 111
The least common multiple (LCM) of 192 and 111 is 7104.
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 192 and 111?
First, calculate the GCD of 192 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 111 = 1 remainder 81 |
| 2 | 111 ÷ 81 = 1 remainder 30 |
| 3 | 81 ÷ 30 = 2 remainder 21 |
| 4 | 30 ÷ 21 = 1 remainder 9 |
| 5 | 21 ÷ 9 = 2 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 121 | 2420 |
| 187 and 189 | 35343 |
| 159 and 125 | 19875 |
| 84 and 34 | 1428 |
| 23 and 189 | 4347 |