Least Common Multiple (LCM) of 27 and 85
The least common multiple (LCM) of 27 and 85 is 2295.
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 27 and 85?
First, calculate the GCD of 27 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 85 = 0 remainder 27 |
| 2 | 85 ÷ 27 = 3 remainder 4 |
| 3 | 27 ÷ 4 = 6 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 127 | 22225 |
| 112 and 75 | 8400 |
| 156 and 106 | 8268 |
| 161 and 126 | 2898 |
| 28 and 30 | 420 |