Least Common Multiple (LCM) of 97 and 112
The least common multiple (LCM) of 97 and 112 is 10864.
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 112?
First, calculate the GCD of 97 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 112 = 0 remainder 97 |
| 2 | 112 ÷ 97 = 1 remainder 15 |
| 3 | 97 ÷ 15 = 6 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 105 | 1680 |
| 105 and 105 | 105 |
| 170 and 44 | 3740 |
| 38 and 169 | 6422 |
| 97 and 69 | 6693 |