Least Common Multiple (LCM) of 42 and 191
The least common multiple (LCM) of 42 and 191 is 8022.
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 191?
First, calculate the GCD of 42 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 191 = 0 remainder 42 |
| 2 | 191 ÷ 42 = 4 remainder 23 |
| 3 | 42 ÷ 23 = 1 remainder 19 |
| 4 | 23 ÷ 19 = 1 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 194 | 27742 |
| 172 and 113 | 19436 |
| 31 and 152 | 4712 |
| 168 and 75 | 4200 |
| 110 and 20 | 220 |