Least Common Multiple (LCM) of 155 and 199
The least common multiple (LCM) of 155 and 199 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 155 and 199?
First, calculate the GCD of 155 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 199 = 0 remainder 155 |
| 2 | 199 ÷ 155 = 1 remainder 44 |
| 3 | 155 ÷ 44 = 3 remainder 23 |
| 4 | 44 ÷ 23 = 1 remainder 21 |
| 5 | 23 ÷ 21 = 1 remainder 2 |
| 6 | 21 ÷ 2 = 10 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 34 | 3094 |
| 61 and 131 | 7991 |
| 71 and 101 | 7171 |
| 23 and 168 | 3864 |
| 20 and 50 | 100 |