Least Common Multiple (LCM) of 54 and 192
The least common multiple (LCM) of 54 and 192 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 54 and 192?
First, calculate the GCD of 54 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 192 = 0 remainder 54 |
| 2 | 192 ÷ 54 = 3 remainder 30 |
| 3 | 54 ÷ 30 = 1 remainder 24 |
| 4 | 30 ÷ 24 = 1 remainder 6 |
| 5 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 105 | 420 |
| 63 and 148 | 9324 |
| 148 and 157 | 23236 |
| 88 and 111 | 9768 |
| 188 and 19 | 3572 |