Least Common Multiple (LCM) of 19 and 143
The least common multiple (LCM) of 19 and 143 is 2717.
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 143?
First, calculate the GCD of 19 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 143 = 0 remainder 19 |
| 2 | 143 ÷ 19 = 7 remainder 10 |
| 3 | 19 ÷ 10 = 1 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 31 | 744 |
| 100 and 73 | 7300 |
| 52 and 14 | 364 |
| 178 and 154 | 13706 |
| 60 and 47 | 2820 |