Least Common Multiple (LCM) of 32 and 57
The least common multiple (LCM) of 32 and 57 is 1824.
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 57?
First, calculate the GCD of 32 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 57 = 0 remainder 32 |
| 2 | 57 ÷ 32 = 1 remainder 25 |
| 3 | 32 ÷ 25 = 1 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 80 | 4880 |
| 194 and 78 | 7566 |
| 27 and 66 | 594 |
| 141 and 155 | 21855 |
| 85 and 52 | 4420 |