Least Common Multiple (LCM) of 54 and 86
The least common multiple (LCM) of 54 and 86 is 2322.
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 54 and 86?
First, calculate the GCD of 54 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 86 = 0 remainder 54 |
| 2 | 86 ÷ 54 = 1 remainder 32 |
| 3 | 54 ÷ 32 = 1 remainder 22 |
| 4 | 32 ÷ 22 = 1 remainder 10 |
| 5 | 22 ÷ 10 = 2 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 112 | 1456 |
| 165 and 157 | 25905 |
| 161 and 154 | 3542 |
| 93 and 161 | 14973 |
| 28 and 186 | 2604 |