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 |
|---|---|
| 120 and 57 | 2280 |
| 55 and 86 | 4730 |
| 176 and 87 | 15312 |
| 100 and 156 | 3900 |
| 112 and 175 | 2800 |