Least Common Multiple (LCM) of 149 and 109
The least common multiple (LCM) of 149 and 109 is 16241.
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 149 and 109?
First, calculate the GCD of 149 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 109 = 1 remainder 40 |
| 2 | 109 ÷ 40 = 2 remainder 29 |
| 3 | 40 ÷ 29 = 1 remainder 11 |
| 4 | 29 ÷ 11 = 2 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 175 | 25200 |
| 74 and 113 | 8362 |
| 42 and 61 | 2562 |
| 177 and 25 | 4425 |
| 31 and 163 | 5053 |