Least Common Multiple (LCM) of 185 and 38
The least common multiple (LCM) of 185 and 38 is 7030.
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 38?
First, calculate the GCD of 185 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 38 = 4 remainder 33 |
| 2 | 38 ÷ 33 = 1 remainder 5 |
| 3 | 33 ÷ 5 = 6 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 172 | 11180 |
| 164 and 172 | 7052 |
| 112 and 177 | 19824 |
| 159 and 186 | 9858 |
| 105 and 148 | 15540 |