Least Common Multiple (LCM) of 97 and 103
The least common multiple (LCM) of 97 and 103 is 9991.
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 103?
First, calculate the GCD of 97 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 103 = 0 remainder 97 |
| 2 | 103 ÷ 97 = 1 remainder 6 |
| 3 | 97 ÷ 6 = 16 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 176 | 9328 |
| 184 and 135 | 24840 |
| 18 and 40 | 360 |
| 197 and 122 | 24034 |
| 125 and 146 | 18250 |