Least Common Multiple (LCM) of 19 and 109
The least common multiple (LCM) of 19 and 109 is 2071.
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 19 and 109?
First, calculate the GCD of 19 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 109 = 0 remainder 19 |
| 2 | 109 ÷ 19 = 5 remainder 14 |
| 3 | 19 ÷ 14 = 1 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 125 | 24000 |
| 200 and 110 | 2200 |
| 137 and 122 | 16714 |
| 128 and 130 | 8320 |
| 14 and 181 | 2534 |