Least Common Multiple (LCM) of 19 and 73
The least common multiple (LCM) of 19 and 73 is 1387.
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 73?
First, calculate the GCD of 19 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 73 = 0 remainder 19 |
| 2 | 73 ÷ 19 = 3 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 |
|---|---|
| 101 and 57 | 5757 |
| 170 and 126 | 10710 |
| 12 and 20 | 60 |
| 123 and 35 | 4305 |
| 25 and 118 | 2950 |