Least Common Multiple (LCM) of 169 and 97
The least common multiple (LCM) of 169 and 97 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 169 and 97?
First, calculate the GCD of 169 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 97 = 1 remainder 72 |
| 2 | 97 ÷ 72 = 1 remainder 25 |
| 3 | 72 ÷ 25 = 2 remainder 22 |
| 4 | 25 ÷ 22 = 1 remainder 3 |
| 5 | 22 ÷ 3 = 7 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 59 | 7965 |
| 170 and 10 | 170 |
| 196 and 24 | 1176 |
| 98 and 56 | 392 |
| 72 and 158 | 5688 |