Least Common Multiple (LCM) of 96 and 175
The least common multiple (LCM) of 96 and 175 is 16800.
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 96 and 175?
First, calculate the GCD of 96 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 175 = 0 remainder 96 |
| 2 | 175 ÷ 96 = 1 remainder 79 |
| 3 | 96 ÷ 79 = 1 remainder 17 |
| 4 | 79 ÷ 17 = 4 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 79 | 1264 |
| 123 and 28 | 3444 |
| 121 and 192 | 23232 |
| 164 and 77 | 12628 |
| 117 and 181 | 21177 |