Least Common Multiple (LCM) of 105 and 44
The least common multiple (LCM) of 105 and 44 is 4620.
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 44?
First, calculate the GCD of 105 and 44 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 44 = 2 remainder 17 |
| 2 | 44 ÷ 17 = 2 remainder 10 |
| 3 | 17 ÷ 10 = 1 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 22 | 2926 |
| 97 and 61 | 5917 |
| 14 and 189 | 378 |
| 178 and 21 | 3738 |
| 66 and 16 | 528 |