Least Common Multiple (LCM) of 105 and 196
The least common multiple (LCM) of 105 and 196 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 105 and 196?
First, calculate the GCD of 105 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 196 = 0 remainder 105 |
| 2 | 196 ÷ 105 = 1 remainder 91 |
| 3 | 105 ÷ 91 = 1 remainder 14 |
| 4 | 91 ÷ 14 = 6 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 14 | 938 |
| 14 and 74 | 518 |
| 159 and 137 | 21783 |
| 162 and 125 | 20250 |
| 105 and 53 | 5565 |