Least Common Multiple (LCM) of 163 and 106
The least common multiple (LCM) of 163 and 106 is 17278.
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 106?
First, calculate the GCD of 163 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 106 = 1 remainder 57 |
| 2 | 106 ÷ 57 = 1 remainder 49 |
| 3 | 57 ÷ 49 = 1 remainder 8 |
| 4 | 49 ÷ 8 = 6 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 180 | 1260 |
| 17 and 121 | 2057 |
| 82 and 118 | 4838 |
| 117 and 112 | 13104 |
| 73 and 199 | 14527 |