Least Common Multiple (LCM) of 19 and 89
The least common multiple (LCM) of 19 and 89 is 1691.
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 89?
First, calculate the GCD of 19 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 89 = 0 remainder 19 |
| 2 | 89 ÷ 19 = 4 remainder 13 |
| 3 | 19 ÷ 13 = 1 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 82 | 820 |
| 173 and 144 | 24912 |
| 60 and 86 | 2580 |
| 167 and 32 | 5344 |
| 69 and 98 | 6762 |