Least Common Multiple (LCM) of 97 and 172
The least common multiple (LCM) of 97 and 172 is 16684.
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 172?
First, calculate the GCD of 97 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 172 = 0 remainder 97 |
| 2 | 172 ÷ 97 = 1 remainder 75 |
| 3 | 97 ÷ 75 = 1 remainder 22 |
| 4 | 75 ÷ 22 = 3 remainder 9 |
| 5 | 22 ÷ 9 = 2 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 124 | 8060 |
| 198 and 199 | 39402 |
| 72 and 56 | 504 |
| 70 and 72 | 2520 |
| 173 and 126 | 21798 |