Least Common Multiple (LCM) of 19 and 54
The least common multiple (LCM) of 19 and 54 is 1026.
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 54?
First, calculate the GCD of 19 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 54 = 0 remainder 19 |
| 2 | 54 ÷ 19 = 2 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 |
|---|---|
| 158 and 52 | 4108 |
| 160 and 55 | 1760 |
| 60 and 188 | 2820 |
| 125 and 182 | 22750 |
| 149 and 101 | 15049 |