Least Common Multiple (LCM) of 102 and 196
The least common multiple (LCM) of 102 and 196 is 9996.
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 102 and 196?
First, calculate the GCD of 102 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 196 = 0 remainder 102 |
| 2 | 196 ÷ 102 = 1 remainder 94 |
| 3 | 102 ÷ 94 = 1 remainder 8 |
| 4 | 94 ÷ 8 = 11 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 36 | 1044 |
| 60 and 25 | 300 |
| 129 and 177 | 7611 |
| 144 and 110 | 7920 |
| 99 and 70 | 6930 |