Least Common Multiple (LCM) of 175 and 97
The least common multiple (LCM) of 175 and 97 is 16975.
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 175 and 97?
First, calculate the GCD of 175 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 97 = 1 remainder 78 |
| 2 | 97 ÷ 78 = 1 remainder 19 |
| 3 | 78 ÷ 19 = 4 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 109 | 19511 |
| 197 and 146 | 28762 |
| 160 and 87 | 13920 |
| 33 and 45 | 495 |
| 69 and 94 | 6486 |