Least Common Multiple (LCM) of 84 and 57
The least common multiple (LCM) of 84 and 57 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 84 and 57?
First, calculate the GCD of 84 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 57 = 1 remainder 27 |
| 2 | 57 ÷ 27 = 2 remainder 3 |
| 3 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 141 | 7332 |
| 71 and 184 | 13064 |
| 89 and 45 | 4005 |
| 187 and 111 | 20757 |
| 116 and 111 | 12876 |