Least Common Multiple (LCM) of 97 and 109
The least common multiple (LCM) of 97 and 109 is 10573.
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 109?
First, calculate the GCD of 97 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 109 = 0 remainder 97 |
| 2 | 109 ÷ 97 = 1 remainder 12 |
| 3 | 97 ÷ 12 = 8 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 35 | 4340 |
| 100 and 31 | 3100 |
| 76 and 51 | 3876 |
| 193 and 172 | 33196 |
| 198 and 159 | 10494 |