Least Common Multiple (LCM) of 42 and 199
The least common multiple (LCM) of 42 and 199 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 42 and 199?
First, calculate the GCD of 42 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 199 = 0 remainder 42 |
| 2 | 199 ÷ 42 = 4 remainder 31 |
| 3 | 42 ÷ 31 = 1 remainder 11 |
| 4 | 31 ÷ 11 = 2 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 161 | 30590 |
| 134 and 67 | 134 |
| 112 and 101 | 11312 |
| 136 and 170 | 680 |
| 189 and 155 | 29295 |