Least Common Multiple (LCM) of 97 and 175
The least common multiple (LCM) of 97 and 175 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 97 and 175?
First, calculate the GCD of 97 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 175 = 0 remainder 97 |
| 2 | 175 ÷ 97 = 1 remainder 78 |
| 3 | 97 ÷ 78 = 1 remainder 19 |
| 4 | 78 ÷ 19 = 4 remainder 2 |
| 5 | 19 ÷ 2 = 9 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 135 | 8640 |
| 14 and 48 | 336 |
| 195 and 102 | 6630 |
| 112 and 157 | 17584 |
| 140 and 79 | 11060 |