Least Common Multiple (LCM) of 196 and 102
The least common multiple (LCM) of 196 and 102 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 196 and 102?
First, calculate the GCD of 196 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 102 = 1 remainder 94 |
| 2 | 102 ÷ 94 = 1 remainder 8 |
| 3 | 94 ÷ 8 = 11 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 128 | 5760 |
| 128 and 128 | 128 |
| 39 and 114 | 1482 |
| 156 and 115 | 17940 |
| 114 and 70 | 3990 |