Least Common Multiple (LCM) of 97 and 173
The least common multiple (LCM) of 97 and 173 is 16781.
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 173?
First, calculate the GCD of 97 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 173 = 0 remainder 97 |
| 2 | 173 ÷ 97 = 1 remainder 76 |
| 3 | 97 ÷ 76 = 1 remainder 21 |
| 4 | 76 ÷ 21 = 3 remainder 13 |
| 5 | 21 ÷ 13 = 1 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 181 | 8326 |
| 43 and 112 | 4816 |
| 33 and 36 | 396 |
| 103 and 30 | 3090 |
| 85 and 10 | 170 |