Least Common Multiple (LCM) of 196 and 105
The least common multiple (LCM) of 196 and 105 is 2940.
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 196 and 105?
First, calculate the GCD of 196 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 105 = 1 remainder 91 |
| 2 | 105 ÷ 91 = 1 remainder 14 |
| 3 | 91 ÷ 14 = 6 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 142 | 2982 |
| 176 and 169 | 29744 |
| 21 and 67 | 1407 |
| 175 and 158 | 27650 |
| 105 and 34 | 3570 |