Least Common Multiple (LCM) of 105 and 49
The least common multiple (LCM) of 105 and 49 is 735.
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 49?
First, calculate the GCD of 105 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 49 = 2 remainder 7 |
| 2 | 49 ÷ 7 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 22 | 1958 |
| 189 and 39 | 2457 |
| 40 and 149 | 5960 |
| 105 and 183 | 6405 |
| 24 and 100 | 600 |