Least Common Multiple (LCM) of 42 and 163
The least common multiple (LCM) of 42 and 163 is 6846.
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 163?
First, calculate the GCD of 42 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 163 = 0 remainder 42 |
| 2 | 163 ÷ 42 = 3 remainder 37 |
| 3 | 42 ÷ 37 = 1 remainder 5 |
| 4 | 37 ÷ 5 = 7 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 107 | 4601 |
| 82 and 62 | 2542 |
| 123 and 135 | 5535 |
| 32 and 109 | 3488 |
| 29 and 37 | 1073 |