Least Common Multiple (LCM) of 199 and 42
The least common multiple (LCM) of 199 and 42 is 8358.
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 42?
First, calculate the GCD of 199 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 42 = 4 remainder 31 |
| 2 | 42 ÷ 31 = 1 remainder 11 |
| 3 | 31 ÷ 11 = 2 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 10 | 130 |
| 171 and 154 | 26334 |
| 151 and 93 | 14043 |
| 156 and 14 | 1092 |
| 101 and 137 | 13837 |