Least Common Multiple (LCM) of 105 and 149
The least common multiple (LCM) of 105 and 149 is 15645.
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 105 and 149?
First, calculate the GCD of 105 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 149 = 0 remainder 105 |
| 2 | 149 ÷ 105 = 1 remainder 44 |
| 3 | 105 ÷ 44 = 2 remainder 17 |
| 4 | 44 ÷ 17 = 2 remainder 10 |
| 5 | 17 ÷ 10 = 1 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 178 | 6230 |
| 132 and 36 | 396 |
| 172 and 34 | 2924 |
| 91 and 34 | 3094 |
| 167 and 51 | 8517 |