Least Common Multiple (LCM) of 54 and 89
The least common multiple (LCM) of 54 and 89 is 4806.
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 89?
First, calculate the GCD of 54 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 89 = 0 remainder 54 |
| 2 | 89 ÷ 54 = 1 remainder 35 |
| 3 | 54 ÷ 35 = 1 remainder 19 |
| 4 | 35 ÷ 19 = 1 remainder 16 |
| 5 | 19 ÷ 16 = 1 remainder 3 |
| 6 | 16 ÷ 3 = 5 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 170 | 11220 |
| 27 and 106 | 2862 |
| 14 and 60 | 420 |
| 167 and 182 | 30394 |
| 152 and 27 | 4104 |