Least Common Multiple (LCM) of 106 and 166
The least common multiple (LCM) of 106 and 166 is 8798.
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 166?
First, calculate the GCD of 106 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 166 = 0 remainder 106 |
| 2 | 166 ÷ 106 = 1 remainder 60 |
| 3 | 106 ÷ 60 = 1 remainder 46 |
| 4 | 60 ÷ 46 = 1 remainder 14 |
| 5 | 46 ÷ 14 = 3 remainder 4 |
| 6 | 14 ÷ 4 = 3 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 144 | 2448 |
| 175 and 99 | 17325 |
| 180 and 123 | 7380 |
| 88 and 134 | 5896 |
| 15 and 18 | 90 |