Least Common Multiple (LCM) of 18 and 85
The least common multiple (LCM) of 18 and 85 is 1530.
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 18 and 85?
First, calculate the GCD of 18 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 85 = 0 remainder 18 |
| 2 | 85 ÷ 18 = 4 remainder 13 |
| 3 | 18 ÷ 13 = 1 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 130 | 10660 |
| 152 and 163 | 24776 |
| 64 and 105 | 6720 |
| 172 and 106 | 9116 |
| 191 and 123 | 23493 |