Least Common Multiple (LCM) of 57 and 96
The least common multiple (LCM) of 57 and 96 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 57 and 96?
First, calculate the GCD of 57 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 96 = 0 remainder 57 |
| 2 | 96 ÷ 57 = 1 remainder 39 |
| 3 | 57 ÷ 39 = 1 remainder 18 |
| 4 | 39 ÷ 18 = 2 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 137 | 5480 |
| 12 and 63 | 252 |
| 39 and 15 | 195 |
| 152 and 69 | 10488 |
| 186 and 102 | 3162 |