lcm of 24 and 60

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 24 and 60. We will find the LCM by determining the multiples of each number and identifying the smallest common multiple.

Answer

$120$

Steps to Solve

List the multiples of each number

First, we will list the multiples of 24 and 60 to identify the smallest common multiple.

Multiples of 24:

$24, 48, 72, 96, 120, 144, 168, ...$

Multiples of 60:

$60, 120, 180, 240, ...$

Identify the common multiples

Next, we will find the common multiples from the lists we created above.

Observing the two lists, we can see that the common multiples are:

$120, 240, ...$

Find the least common multiple

The least common multiple (LCM) is the smallest number that appears in both lists. From the common multiples identified, the smallest is:

$$ LCM(24, 60) = 120 $$

The least common multiple (LCM) of 24 and 60 is $120$.

More Information

The least common multiple is useful in various mathematical applications, including adding and subtracting fractions and solving problems involving ratios. The LCM helps in finding the lowest common denominator.

Tips

A common mistake is to confuse LCM with GCD (Greatest Common Divisor). Ensure to differentiate between the two concepts.
Another mistake is to list too few multiples. Always check enough multiples to find the LCM.

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