Least Common Multiple (LCM) of 32 and 199
The least common multiple (LCM) of 32 and 199 is 6368.
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 32 and 199?
First, calculate the GCD of 32 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 199 = 0 remainder 32 |
| 2 | 199 ÷ 32 = 6 remainder 7 |
| 3 | 32 ÷ 7 = 4 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 75 | 14925 |
| 29 and 54 | 1566 |
| 171 and 117 | 2223 |
| 70 and 54 | 1890 |
| 179 and 153 | 27387 |