Least Common Multiple (LCM) of 192 and 54
The least common multiple (LCM) of 192 and 54 is 1728.
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 54?
First, calculate the GCD of 192 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 54 = 3 remainder 30 |
| 2 | 54 ÷ 30 = 1 remainder 24 |
| 3 | 30 ÷ 24 = 1 remainder 6 |
| 4 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 69 | 4623 |
| 168 and 57 | 3192 |
| 85 and 25 | 425 |
| 115 and 162 | 18630 |
| 41 and 110 | 4510 |