Least Common Multiple (LCM) of 192 and 89
The least common multiple (LCM) of 192 and 89 is 17088.
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 89?
First, calculate the GCD of 192 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 89 = 2 remainder 14 |
| 2 | 89 ÷ 14 = 6 remainder 5 |
| 3 | 14 ÷ 5 = 2 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 142 | 4970 |
| 30 and 192 | 960 |
| 14 and 86 | 602 |
| 135 and 118 | 15930 |
| 144 and 137 | 19728 |