Least Common Multiple (LCM) of 54 and 85
The least common multiple (LCM) of 54 and 85 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 85?
First, calculate the GCD of 54 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 85 = 0 remainder 54 |
| 2 | 85 ÷ 54 = 1 remainder 31 |
| 3 | 54 ÷ 31 = 1 remainder 23 |
| 4 | 31 ÷ 23 = 1 remainder 8 |
| 5 | 23 ÷ 8 = 2 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 86 | 7310 |
| 102 and 139 | 14178 |
| 103 and 117 | 12051 |
| 141 and 10 | 1410 |
| 49 and 110 | 5390 |