Least Common Multiple (LCM) of 185 and 108
The least common multiple (LCM) of 185 and 108 is 19980.
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 185 and 108?
First, calculate the GCD of 185 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 108 = 1 remainder 77 |
| 2 | 108 ÷ 77 = 1 remainder 31 |
| 3 | 77 ÷ 31 = 2 remainder 15 |
| 4 | 31 ÷ 15 = 2 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 73 | 3285 |
| 73 and 20 | 1460 |
| 113 and 15 | 1695 |
| 87 and 183 | 5307 |
| 24 and 40 | 120 |