Least Common Multiple (LCM) of 192 and 178
The least common multiple (LCM) of 192 and 178 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 178?
First, calculate the GCD of 192 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 178 = 1 remainder 14 |
| 2 | 178 ÷ 14 = 12 remainder 10 |
| 3 | 14 ÷ 10 = 1 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 45 | 360 |
| 125 and 173 | 21625 |
| 182 and 76 | 6916 |
| 119 and 153 | 1071 |
| 80 and 120 | 240 |