Least Common Multiple (LCM) of 163 and 142
The least common multiple (LCM) of 163 and 142 is 23146.
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 163 and 142?
First, calculate the GCD of 163 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 142 = 1 remainder 21 |
| 2 | 142 ÷ 21 = 6 remainder 16 |
| 3 | 21 ÷ 16 = 1 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 70 | 210 |
| 102 and 51 | 102 |
| 16 and 154 | 1232 |
| 45 and 19 | 855 |
| 185 and 31 | 5735 |