Least Common Multiple (LCM) of 85 and 108
The least common multiple (LCM) of 85 and 108 is 9180.
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 85 and 108?
First, calculate the GCD of 85 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 108 = 0 remainder 85 |
| 2 | 108 ÷ 85 = 1 remainder 23 |
| 3 | 85 ÷ 23 = 3 remainder 16 |
| 4 | 23 ÷ 16 = 1 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 20 | 3380 |
| 132 and 53 | 6996 |
| 23 and 171 | 3933 |
| 73 and 23 | 1679 |
| 69 and 149 | 10281 |