Least Common Multiple (LCM) of 97 and 128
The least common multiple (LCM) of 97 and 128 is 12416.
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 128?
First, calculate the GCD of 97 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 128 = 0 remainder 97 |
| 2 | 128 ÷ 97 = 1 remainder 31 |
| 3 | 97 ÷ 31 = 3 remainder 4 |
| 4 | 31 ÷ 4 = 7 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 176 | 15664 |
| 196 and 109 | 21364 |
| 102 and 181 | 18462 |
| 122 and 167 | 20374 |
| 184 and 150 | 13800 |