Least Common Multiple (LCM) of 19 and 74
The least common multiple (LCM) of 19 and 74 is 1406.
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 74?
First, calculate the GCD of 19 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 74 = 0 remainder 19 |
| 2 | 74 ÷ 19 = 3 remainder 17 |
| 3 | 19 ÷ 17 = 1 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 127 | 19812 |
| 117 and 72 | 936 |
| 161 and 198 | 31878 |
| 84 and 162 | 2268 |
| 189 and 36 | 756 |