Least Common Multiple (LCM) of 199 and 145
The least common multiple (LCM) of 199 and 145 is 28855.
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 145?
First, calculate the GCD of 199 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 145 = 1 remainder 54 |
| 2 | 145 ÷ 54 = 2 remainder 37 |
| 3 | 54 ÷ 37 = 1 remainder 17 |
| 4 | 37 ÷ 17 = 2 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 140 | 18060 |
| 42 and 41 | 1722 |
| 130 and 138 | 8970 |
| 13 and 64 | 832 |
| 45 and 162 | 810 |