Least Common Multiple (LCM) of 54 and 84
The least common multiple (LCM) of 54 and 84 is 756.
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 84?
First, calculate the GCD of 54 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 84 = 0 remainder 54 |
| 2 | 84 ÷ 54 = 1 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 |
|---|---|
| 86 and 54 | 2322 |
| 188 and 188 | 188 |
| 91 and 88 | 8008 |
| 133 and 27 | 3591 |
| 47 and 145 | 6815 |