Least Common Multiple (LCM) of 19 and 24
The least common multiple (LCM) of 19 and 24 is 456.
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 24?
First, calculate the GCD of 19 and 24 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 24 = 0 remainder 19 |
| 2 | 24 ÷ 19 = 1 remainder 5 |
| 3 | 19 ÷ 5 = 3 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 162 | 4050 |
| 178 and 187 | 33286 |
| 14 and 197 | 2758 |
| 48 and 169 | 8112 |
| 168 and 166 | 13944 |