Least Common Multiple (LCM) of 54 and 66
The least common multiple (LCM) of 54 and 66 is 594.
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 66?
First, calculate the GCD of 54 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 66 = 0 remainder 54 |
| 2 | 66 ÷ 54 = 1 remainder 12 |
| 3 | 54 ÷ 12 = 4 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 75 | 14550 |
| 170 and 126 | 10710 |
| 81 and 160 | 12960 |
| 41 and 179 | 7339 |
| 105 and 98 | 1470 |