Least Common Multiple (LCM) of 106 and 164
The least common multiple (LCM) of 106 and 164 is 8692.
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 164?
First, calculate the GCD of 106 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 164 = 0 remainder 106 |
| 2 | 164 ÷ 106 = 1 remainder 58 |
| 3 | 106 ÷ 58 = 1 remainder 48 |
| 4 | 58 ÷ 48 = 1 remainder 10 |
| 5 | 48 ÷ 10 = 4 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 110 | 16390 |
| 22 and 132 | 132 |
| 84 and 19 | 1596 |
| 20 and 110 | 220 |
| 45 and 179 | 8055 |