Least Common Multiple (LCM) of 196 and 106
The least common multiple (LCM) of 196 and 106 is 10388.
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 106?
First, calculate the GCD of 196 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 106 = 1 remainder 90 |
| 2 | 106 ÷ 90 = 1 remainder 16 |
| 3 | 90 ÷ 16 = 5 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 180 | 9540 |
| 76 and 105 | 7980 |
| 189 and 98 | 2646 |
| 35 and 63 | 315 |
| 72 and 74 | 2664 |