Least Common Multiple (LCM) of 102 and 97
The least common multiple (LCM) of 102 and 97 is 9894.
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 102 and 97?
First, calculate the GCD of 102 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 97 = 1 remainder 5 |
| 2 | 97 ÷ 5 = 19 remainder 2 |
| 3 | 5 ÷ 2 = 2 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 57 | 342 |
| 105 and 105 | 105 |
| 119 and 75 | 8925 |
| 71 and 87 | 6177 |
| 40 and 44 | 440 |