Least Common Multiple (LCM) of 163 and 113
The least common multiple (LCM) of 163 and 113 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 163 and 113?
First, calculate the GCD of 163 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 113 = 1 remainder 50 |
| 2 | 113 ÷ 50 = 2 remainder 13 |
| 3 | 50 ÷ 13 = 3 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 91 | 1547 |
| 187 and 121 | 2057 |
| 145 and 189 | 27405 |
| 135 and 83 | 11205 |
| 38 and 46 | 874 |