Least Common Multiple (LCM) of 19 and 168
The least common multiple (LCM) of 19 and 168 is 3192.
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 168?
First, calculate the GCD of 19 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 168 = 0 remainder 19 |
| 2 | 168 ÷ 19 = 8 remainder 16 |
| 3 | 19 ÷ 16 = 1 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 81 | 324 |
| 123 and 47 | 5781 |
| 159 and 158 | 25122 |
| 198 and 179 | 35442 |
| 148 and 140 | 5180 |