Least Common Multiple (LCM) of 105 and 185
The least common multiple (LCM) of 105 and 185 is 3885.
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 105 and 185?
First, calculate the GCD of 105 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 185 = 0 remainder 105 |
| 2 | 185 ÷ 105 = 1 remainder 80 |
| 3 | 105 ÷ 80 = 1 remainder 25 |
| 4 | 80 ÷ 25 = 3 remainder 5 |
| 5 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 140 | 7140 |
| 136 and 161 | 21896 |
| 147 and 81 | 3969 |
| 71 and 64 | 4544 |
| 90 and 36 | 180 |