Least Common Multiple (LCM) of 48 and 185
The least common multiple (LCM) of 48 and 185 is 8880.
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 48 and 185?
First, calculate the GCD of 48 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 185 = 0 remainder 48 |
| 2 | 185 ÷ 48 = 3 remainder 41 |
| 3 | 48 ÷ 41 = 1 remainder 7 |
| 4 | 41 ÷ 7 = 5 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 199 | 37014 |
| 40 and 180 | 360 |
| 194 and 113 | 21922 |
| 14 and 40 | 280 |
| 53 and 178 | 9434 |