Least Common Multiple (LCM) of 54 and 32
The least common multiple (LCM) of 54 and 32 is 864.
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 32?
First, calculate the GCD of 54 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 32 = 1 remainder 22 |
| 2 | 32 ÷ 22 = 1 remainder 10 |
| 3 | 22 ÷ 10 = 2 remainder 2 |
| 4 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 67 | 6968 |
| 87 and 106 | 9222 |
| 189 and 149 | 28161 |
| 74 and 36 | 1332 |
| 87 and 185 | 16095 |