Question

Find the least common multiple of 24, 42 and 60.

Answer 1

Hint: The least number which is exactly divisible by each of the given numbers is called the least common multiple amongst the multiple. By proceeding with this definition, we can easily solve the above stated problem.

Complete step-by-step answer:
Factors and Multiples: All the numbers that divide a number completely, i.e., without leaving any remainder, are called factors of that number. Multiples are those numbers which we get after multiplying numbers. For example, consider the number 12, 16, 24. So the factors can be expressed as:$12(2\times 2\times 3),16(2\times 2\times 2\times 2)\text{ and }24(2\times 2\times 2\times 3)$.
To find the LCM of the given numbers, we express each number as a product of prime numbers. The product of highest power of the prime numbers that appear in prime factorization of any of the numbers gives us the LCM.
According to our problem we have 24, 42 and 60. We are required to calculate the least common multiple.
So, the prime factors of 24 are: $24=2\times 2\times 2\times 3$.
The prime factors of 42 are: $42=2\times 3\times 7$.
The prime factors of 60 are: $60=2\times 2\times 3\times 5$.
Hence, the least common multiple of 24, 42 and 60 can be expressed as:
$\begin{align}
  & L.C.M=2\times 2\times 2\times 3\times 5\times 7 \\
 & L.C.M=840 \\
\end{align}$
So, the L.C.M. of 24, 42 and 60 is 840.

Note: The key step in solving this problem is the basic definition of LCM. So, by using the definition and expression in prime factors, we obtained our answer. This knowledge is useful in solving complex problems of mathematics.