Least Common Multiple (LCM) of 199 and 168
The least common multiple (LCM) of 199 and 168 is 33432.
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 199 and 168?
First, calculate the GCD of 199 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 168 = 1 remainder 31 |
| 2 | 168 ÷ 31 = 5 remainder 13 |
| 3 | 31 ÷ 13 = 2 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 31 | 1984 |
| 145 and 84 | 12180 |
| 17 and 86 | 1462 |
| 106 and 32 | 1696 |
| 196 and 37 | 7252 |