Least Common Multiple (LCM) of 105 and 19
The least common multiple (LCM) of 105 and 19 is 1995.
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 19?
First, calculate the GCD of 105 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 19 = 5 remainder 10 |
| 2 | 19 ÷ 10 = 1 remainder 9 |
| 3 | 10 ÷ 9 = 1 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 28 | 756 |
| 58 and 155 | 8990 |
| 148 and 92 | 3404 |
| 155 and 130 | 4030 |
| 200 and 19 | 3800 |