Least Common Multiple (LCM) of 144 and 175
The least common multiple (LCM) of 144 and 175 is 25200.
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 144 and 175?
First, calculate the GCD of 144 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 175 = 0 remainder 144 |
| 2 | 175 ÷ 144 = 1 remainder 31 |
| 3 | 144 ÷ 31 = 4 remainder 20 |
| 4 | 31 ÷ 20 = 1 remainder 11 |
| 5 | 20 ÷ 11 = 1 remainder 9 |
| 6 | 11 ÷ 9 = 1 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 185 | 1480 |
| 128 and 163 | 20864 |
| 146 and 35 | 5110 |
| 196 and 178 | 17444 |
| 77 and 115 | 8855 |