Least Common Multiple (LCM) of 172 and 97
The least common multiple (LCM) of 172 and 97 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 172 and 97?
First, calculate the GCD of 172 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 97 = 1 remainder 75 |
| 2 | 97 ÷ 75 = 1 remainder 22 |
| 3 | 75 ÷ 22 = 3 remainder 9 |
| 4 | 22 ÷ 9 = 2 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 119 | 1547 |
| 42 and 142 | 2982 |
| 51 and 36 | 612 |
| 96 and 19 | 1824 |
| 113 and 112 | 12656 |