Least Common Multiple (LCM) of 168 and 199
The least common multiple (LCM) of 168 and 199 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 168 and 199?
First, calculate the GCD of 168 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 199 = 0 remainder 168 |
| 2 | 199 ÷ 168 = 1 remainder 31 |
| 3 | 168 ÷ 31 = 5 remainder 13 |
| 4 | 31 ÷ 13 = 2 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 71 | 6816 |
| 94 and 136 | 6392 |
| 44 and 109 | 4796 |
| 113 and 180 | 20340 |
| 37 and 42 | 1554 |