Least Common Multiple (LCM) of 105 and 166
The least common multiple (LCM) of 105 and 166 is 17430.
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 105 and 166?
First, calculate the GCD of 105 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 166 = 0 remainder 105 |
| 2 | 166 ÷ 105 = 1 remainder 61 |
| 3 | 105 ÷ 61 = 1 remainder 44 |
| 4 | 61 ÷ 44 = 1 remainder 17 |
| 5 | 44 ÷ 17 = 2 remainder 10 |
| 6 | 17 ÷ 10 = 1 remainder 7 |
| 7 | 10 ÷ 7 = 1 remainder 3 |
| 8 | 7 ÷ 3 = 2 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 126 | 1638 |
| 36 and 42 | 252 |
| 54 and 129 | 2322 |
| 34 and 180 | 3060 |
| 131 and 24 | 3144 |