Least Common Multiple (LCM) of 110 and 192
The least common multiple (LCM) of 110 and 192 is 10560.
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 110 and 192?
First, calculate the GCD of 110 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 192 = 0 remainder 110 |
| 2 | 192 ÷ 110 = 1 remainder 82 |
| 3 | 110 ÷ 82 = 1 remainder 28 |
| 4 | 82 ÷ 28 = 2 remainder 26 |
| 5 | 28 ÷ 26 = 1 remainder 2 |
| 6 | 26 ÷ 2 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 46 | 4462 |
| 51 and 200 | 10200 |
| 42 and 11 | 462 |
| 97 and 109 | 10573 |
| 130 and 88 | 5720 |