Least Common Multiple (LCM) of 199 and 162
The least common multiple (LCM) of 199 and 162 is 32238.
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 162?
First, calculate the GCD of 199 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 162 = 1 remainder 37 |
| 2 | 162 ÷ 37 = 4 remainder 14 |
| 3 | 37 ÷ 14 = 2 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 103 | 20600 |
| 38 and 28 | 532 |
| 75 and 56 | 4200 |
| 110 and 44 | 220 |
| 99 and 105 | 3465 |