Least Common Multiple (LCM) of 106 and 196
The least common multiple (LCM) of 106 and 196 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 106 and 196?
First, calculate the GCD of 106 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 196 = 0 remainder 106 |
| 2 | 196 ÷ 106 = 1 remainder 90 |
| 3 | 106 ÷ 90 = 1 remainder 16 |
| 4 | 90 ÷ 16 = 5 remainder 10 |
| 5 | 16 ÷ 10 = 1 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 43 | 4730 |
| 84 and 139 | 11676 |
| 157 and 60 | 9420 |
| 97 and 70 | 6790 |
| 71 and 150 | 10650 |