Least Common Multiple (LCM) of 30 and 109
The least common multiple (LCM) of 30 and 109 is 3270.
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 30 and 109?
First, calculate the GCD of 30 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 109 = 0 remainder 30 |
| 2 | 109 ÷ 30 = 3 remainder 19 |
| 3 | 30 ÷ 19 = 1 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 200 | 18600 |
| 113 and 166 | 18758 |
| 149 and 51 | 7599 |
| 169 and 68 | 11492 |
| 177 and 47 | 8319 |