Least Common Multiple (LCM) of 19 and 104
The least common multiple (LCM) of 19 and 104 is 1976.
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 104?
First, calculate the GCD of 19 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 104 = 0 remainder 19 |
| 2 | 104 ÷ 19 = 5 remainder 9 |
| 3 | 19 ÷ 9 = 2 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 64 | 2880 |
| 118 and 17 | 2006 |
| 46 and 77 | 3542 |
| 79 and 63 | 4977 |
| 189 and 44 | 8316 |