Least Common Multiple (LCM) of 19 and 52
The least common multiple (LCM) of 19 and 52 is 988.
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 52?
First, calculate the GCD of 19 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 52 = 0 remainder 19 |
| 2 | 52 ÷ 19 = 2 remainder 14 |
| 3 | 19 ÷ 14 = 1 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 185 | 34965 |
| 23 and 165 | 3795 |
| 175 and 12 | 2100 |
| 97 and 81 | 7857 |
| 32 and 70 | 1120 |