Questions: Find the least common multiple of the numbers. 1250 and 1800

Solution Steps

To find the least common multiple (LCM) of a set of numbers, we can use the formula that involves the greatest common divisor (GCD). The LCM of two numbers \(a\) and \(b\) is given by:

\[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \]

For more than two numbers, we can iteratively apply this formula. We will use Python's math.gcd function to compute the GCD and then calculate the LCM.

To find the least common multiple (LCM) of \(1250\) and \(1800\), we first compute their greatest common divisor (GCD):

\[ \text{GCD}(1250, 1800) = 250 \]

Using the LCM formula:

\[ \text{LCM}(1250, 1800) = \frac{|1250 \times 1800|}{\text{GCD}(1250, 1800)} = \frac{2250000}{250} = 9000 \]

Next, we find the LCM of \(9000\) and \(62500\):

\[ \text{GCD}(9000, 62500) = 1000 \]

Applying the LCM formula again:

\[ \text{LCM}(9000, 62500) = \frac{|9000 \times 62500|}{\text{GCD}(9000, 62500)} = \frac{562500000}{1000} = 562500 \]

Now, we compute the LCM of \(562500\) and \(2250000\):

\[ \text{GCD}(562500, 2250000) = 562500 \]

Using the LCM formula:

\[ \text{LCM}(562500, 2250000) = \frac{|562500 \times 2250000|}{\text{GCD}(562500, 2250000)} = \frac{1265625000000}{562500} = 2250000 \]

Final Answer