Least Common Multiple (LCM) of 196 and 103
The least common multiple (LCM) of 196 and 103 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 196 and 103?
First, calculate the GCD of 196 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 103 = 1 remainder 93 |
| 2 | 103 ÷ 93 = 1 remainder 10 |
| 3 | 93 ÷ 10 = 9 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 12 | 372 |
| 140 and 166 | 11620 |
| 12 and 70 | 420 |
| 115 and 60 | 1380 |
| 107 and 111 | 11877 |