Least Common Multiple (LCM) of 19 and 106
The least common multiple (LCM) of 19 and 106 is 2014.
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 106?
First, calculate the GCD of 19 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 106 = 0 remainder 19 |
| 2 | 106 ÷ 19 = 5 remainder 11 |
| 3 | 19 ÷ 11 = 1 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 98 | 9506 |
| 26 and 144 | 1872 |
| 33 and 43 | 1419 |
| 140 and 164 | 5740 |
| 54 and 133 | 7182 |