Least Common Multiple (LCM) of 54 and 170
The least common multiple (LCM) of 54 and 170 is 4590.
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 170?
First, calculate the GCD of 54 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 170 = 0 remainder 54 |
| 2 | 170 ÷ 54 = 3 remainder 8 |
| 3 | 54 ÷ 8 = 6 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 165 | 17655 |
| 147 and 36 | 1764 |
| 45 and 159 | 2385 |
| 124 and 89 | 11036 |
| 52 and 89 | 4628 |