Least Common Multiple (LCM) of 19 and 57
The least common multiple (LCM) of 19 and 57 is 57.
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 57?
First, calculate the GCD of 19 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 57 = 0 remainder 19 |
| 2 | 57 ÷ 19 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 100 | 15300 |
| 90 and 80 | 720 |
| 191 and 191 | 191 |
| 162 and 191 | 30942 |
| 162 and 165 | 8910 |