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 |
|---|---|
| 20 and 142 | 1420 |
| 165 and 87 | 4785 |
| 174 and 40 | 3480 |
| 146 and 48 | 3504 |
| 159 and 105 | 5565 |