Least Common Multiple (LCM) of 199 and 154
The least common multiple (LCM) of 199 and 154 is 30646.
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 154?
First, calculate the GCD of 199 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 154 = 1 remainder 45 |
| 2 | 154 ÷ 45 = 3 remainder 19 |
| 3 | 45 ÷ 19 = 2 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 123 | 17220 |
| 69 and 131 | 9039 |
| 147 and 66 | 3234 |
| 123 and 64 | 7872 |
| 189 and 91 | 2457 |