Least Common Multiple (LCM) of 19 and 91
The least common multiple (LCM) of 19 and 91 is 1729.
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 91?
First, calculate the GCD of 19 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 91 = 0 remainder 19 |
| 2 | 91 ÷ 19 = 4 remainder 15 |
| 3 | 19 ÷ 15 = 1 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 49 | 441 |
| 72 and 18 | 72 |
| 182 and 114 | 10374 |
| 97 and 121 | 11737 |
| 105 and 142 | 14910 |