Least Common Multiple (LCM) of 109 and 149
The least common multiple (LCM) of 109 and 149 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 109 and 149?
First, calculate the GCD of 109 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 149 = 0 remainder 109 |
| 2 | 149 ÷ 109 = 1 remainder 40 |
| 3 | 109 ÷ 40 = 2 remainder 29 |
| 4 | 40 ÷ 29 = 1 remainder 11 |
| 5 | 29 ÷ 11 = 2 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 149 | 23989 |
| 53 and 52 | 2756 |
| 177 and 67 | 11859 |
| 83 and 31 | 2573 |
| 75 and 122 | 9150 |