Least Common Multiple (LCM) of 103 and 196
The least common multiple (LCM) of 103 and 196 is 20188.
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 103 and 196?
First, calculate the GCD of 103 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 196 = 0 remainder 103 |
| 2 | 196 ÷ 103 = 1 remainder 93 |
| 3 | 103 ÷ 93 = 1 remainder 10 |
| 4 | 93 ÷ 10 = 9 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 160 | 960 |
| 113 and 154 | 17402 |
| 111 and 121 | 13431 |
| 57 and 171 | 171 |
| 159 and 154 | 24486 |