Least Common Multiple (LCM) of 106 and 163
The least common multiple (LCM) of 106 and 163 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 106 and 163?
First, calculate the GCD of 106 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 163 = 0 remainder 106 |
| 2 | 163 ÷ 106 = 1 remainder 57 |
| 3 | 106 ÷ 57 = 1 remainder 49 |
| 4 | 57 ÷ 49 = 1 remainder 8 |
| 5 | 49 ÷ 8 = 6 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 98 | 3822 |
| 12 and 111 | 444 |
| 33 and 37 | 1221 |
| 15 and 12 | 60 |
| 46 and 41 | 1886 |