Least Common Multiple (LCM) of 199 and 155
The least common multiple (LCM) of 199 and 155 is 30845.
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 155?
First, calculate the GCD of 199 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 155 = 1 remainder 44 |
| 2 | 155 ÷ 44 = 3 remainder 23 |
| 3 | 44 ÷ 23 = 1 remainder 21 |
| 4 | 23 ÷ 21 = 1 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 184 | 9752 |
| 141 and 101 | 14241 |
| 127 and 157 | 19939 |
| 123 and 74 | 9102 |
| 155 and 118 | 18290 |