Least Common Multiple (LCM) of 146 and 192
The least common multiple (LCM) of 146 and 192 is 14016.
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 146 and 192?
First, calculate the GCD of 146 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 146 ÷ 192 = 0 remainder 146 |
| 2 | 192 ÷ 146 = 1 remainder 46 |
| 3 | 146 ÷ 46 = 3 remainder 8 |
| 4 | 46 ÷ 8 = 5 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 48 | 144 |
| 120 and 69 | 2760 |
| 25 and 192 | 4800 |
| 164 and 76 | 3116 |
| 32 and 74 | 1184 |