Least Common Multiple (LCM) of 97 and 169
The least common multiple (LCM) of 97 and 169 is 16393.
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 169?
First, calculate the GCD of 97 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 169 = 0 remainder 97 |
| 2 | 169 ÷ 97 = 1 remainder 72 |
| 3 | 97 ÷ 72 = 1 remainder 25 |
| 4 | 72 ÷ 25 = 2 remainder 22 |
| 5 | 25 ÷ 22 = 1 remainder 3 |
| 6 | 22 ÷ 3 = 7 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 82 | 7462 |
| 130 and 96 | 6240 |
| 170 and 33 | 5610 |
| 96 and 142 | 6816 |
| 38 and 174 | 3306 |