Least Common Multiple (LCM) of 196 and 104
The least common multiple (LCM) of 196 and 104 is 5096.
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 104?
First, calculate the GCD of 196 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 104 = 1 remainder 92 |
| 2 | 104 ÷ 92 = 1 remainder 12 |
| 3 | 92 ÷ 12 = 7 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 120 | 2040 |
| 65 and 52 | 260 |
| 114 and 146 | 8322 |
| 94 and 113 | 10622 |
| 104 and 61 | 6344 |