Least Common Multiple (LCM) of 109 and 166
The least common multiple (LCM) of 109 and 166 is 18094.
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 109 and 166?
First, calculate the GCD of 109 and 166 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 166 = 0 remainder 109 |
| 2 | 166 ÷ 109 = 1 remainder 57 |
| 3 | 109 ÷ 57 = 1 remainder 52 |
| 4 | 57 ÷ 52 = 1 remainder 5 |
| 5 | 52 ÷ 5 = 10 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 105 | 3780 |
| 33 and 138 | 1518 |
| 14 and 77 | 154 |
| 52 and 147 | 7644 |
| 40 and 19 | 760 |