Least Common Multiple (LCM) of 19 and 32
The least common multiple (LCM) of 19 and 32 is 608.
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 32?
First, calculate the GCD of 19 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 32 = 0 remainder 19 |
| 2 | 32 ÷ 19 = 1 remainder 13 |
| 3 | 19 ÷ 13 = 1 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 103 | 10712 |
| 62 and 135 | 8370 |
| 162 and 193 | 31266 |
| 156 and 100 | 3900 |
| 58 and 172 | 4988 |