Least Common Multiple (LCM) of 57 and 84
The least common multiple (LCM) of 57 and 84 is 1596.
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 84?
First, calculate the GCD of 57 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 84 = 0 remainder 57 |
| 2 | 84 ÷ 57 = 1 remainder 27 |
| 3 | 57 ÷ 27 = 2 remainder 3 |
| 4 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 109 | 6213 |
| 17 and 121 | 2057 |
| 32 and 63 | 2016 |
| 139 and 178 | 24742 |
| 170 and 49 | 8330 |