Least Common Multiple (LCM) of 97 and 68
The least common multiple (LCM) of 97 and 68 is 6596.
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 68?
First, calculate the GCD of 97 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 68 = 1 remainder 29 |
| 2 | 68 ÷ 29 = 2 remainder 10 |
| 3 | 29 ÷ 10 = 2 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 117 | 3627 |
| 133 and 182 | 3458 |
| 131 and 125 | 16375 |
| 15 and 131 | 1965 |
| 140 and 14 | 140 |