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 |
|---|---|
| 108 and 190 | 10260 |
| 185 and 164 | 30340 |
| 48 and 142 | 3408 |
| 113 and 191 | 21583 |
| 88 and 72 | 792 |