Least Common Multiple (LCM) of 45 and 166
The least common multiple (LCM) of 45 and 166 is 7470.
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 45 and 166?
First, calculate the GCD of 45 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 166 = 0 remainder 45 |
| 2 | 166 ÷ 45 = 3 remainder 31 |
| 3 | 45 ÷ 31 = 1 remainder 14 |
| 4 | 31 ÷ 14 = 2 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 84 | 588 |
| 86 and 194 | 8342 |
| 146 and 39 | 5694 |
| 197 and 193 | 38021 |
| 133 and 19 | 133 |