Least Common Multiple (LCM) of 106 and 97
The least common multiple (LCM) of 106 and 97 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 106 and 97?
First, calculate the GCD of 106 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 97 = 1 remainder 9 |
| 2 | 97 ÷ 9 = 10 remainder 7 |
| 3 | 9 ÷ 7 = 1 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 87 | 5655 |
| 187 and 193 | 36091 |
| 176 and 159 | 27984 |
| 69 and 142 | 9798 |
| 84 and 131 | 11004 |