Questions: Find the LCM of this set of numbers. 30 and 40

Find the LCM of this set of numbers. 30 and 40
Transcript text: Find the LCM of this set of numbers. 30 and 40
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Solution

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Solution Steps

To find the Least Common Multiple (LCM) of two numbers, we can use the relationship between the LCM and the Greatest Common Divisor (GCD). The LCM of two numbers can be calculated by dividing the product of the numbers by their GCD.

Step 1: Identify the Relationship Between LCM and GCD

To find the Least Common Multiple (LCM) of two numbers, we use the relationship between the LCM and the Greatest Common Divisor (GCD). The formula is given by:

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

Step 2: Calculate the GCD of 30 and 40

The GCD of two numbers is the largest number that divides both of them without leaving a remainder. For 30 and 40, the GCD is 10.

Step 3: Calculate the LCM Using the Formula

Substitute the values into the LCM formula:

\[ \text{LCM}(30, 40) = \frac{|30 \times 40|}{10} = \frac{1200}{10} = 120 \]

Final Answer

The LCM of 30 and 40 is \(\boxed{120}\).

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