Least Common Multiple (LCM) of 113 and 163
The least common multiple (LCM) of 113 and 163 is 18419.
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 113 and 163?
First, calculate the GCD of 113 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 163 = 0 remainder 113 |
| 2 | 163 ÷ 113 = 1 remainder 50 |
| 3 | 113 ÷ 50 = 2 remainder 13 |
| 4 | 50 ÷ 13 = 3 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 26 | 1092 |
| 187 and 146 | 27302 |
| 145 and 189 | 27405 |
| 167 and 167 | 167 |
| 67 and 114 | 7638 |