Least Common Multiple (LCM) of 164 and 199
The least common multiple (LCM) of 164 and 199 is 32636.
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 164 and 199?
First, calculate the GCD of 164 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 199 = 0 remainder 164 |
| 2 | 199 ÷ 164 = 1 remainder 35 |
| 3 | 164 ÷ 35 = 4 remainder 24 |
| 4 | 35 ÷ 24 = 1 remainder 11 |
| 5 | 24 ÷ 11 = 2 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 64 | 7872 |
| 116 and 168 | 4872 |
| 130 and 199 | 25870 |
| 25 and 105 | 525 |
| 104 and 150 | 7800 |