Least Common Multiple (LCM) of 97 and 106
The least common multiple (LCM) of 97 and 106 is 10282.
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 97 and 106?
First, calculate the GCD of 97 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 106 = 0 remainder 97 |
| 2 | 106 ÷ 97 = 1 remainder 9 |
| 3 | 97 ÷ 9 = 10 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 178 | 14062 |
| 198 and 194 | 19206 |
| 20 and 153 | 3060 |
| 166 and 22 | 1826 |
| 133 and 161 | 3059 |