Least Common Multiple (LCM) of 109 and 30
The least common multiple (LCM) of 109 and 30 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 109 and 30?
First, calculate the GCD of 109 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 30 = 3 remainder 19 |
| 2 | 30 ÷ 19 = 1 remainder 11 |
| 3 | 19 ÷ 11 = 1 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 93 | 13578 |
| 143 and 198 | 2574 |
| 115 and 158 | 18170 |
| 178 and 94 | 8366 |
| 104 and 83 | 8632 |