Least Common Multiple (LCM) of 149 and 105
The least common multiple (LCM) of 149 and 105 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 149 and 105?
First, calculate the GCD of 149 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 105 = 1 remainder 44 |
| 2 | 105 ÷ 44 = 2 remainder 17 |
| 3 | 44 ÷ 17 = 2 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 26 | 650 |
| 32 and 150 | 2400 |
| 136 and 23 | 3128 |
| 123 and 48 | 1968 |
| 180 and 66 | 1980 |