Least Common Multiple (LCM) of 32 and 54
The least common multiple (LCM) of 32 and 54 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 32 and 54?
First, calculate the GCD of 32 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 54 = 0 remainder 32 |
| 2 | 54 ÷ 32 = 1 remainder 22 |
| 3 | 32 ÷ 22 = 1 remainder 10 |
| 4 | 22 ÷ 10 = 2 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 89 | 5785 |
| 119 and 32 | 3808 |
| 25 and 69 | 1725 |
| 10 and 108 | 540 |
| 133 and 64 | 8512 |