Question

Find the L.C.M of the numbers 64, 36 and 80?
(a) 1880
(b) 2880
(c) 2550
(d) 3600

Answer 1

Hint: We start solving the problem by recalling the definition of L.C.M (Least common multiple) as the smallest number that can be divided by all the given numbers. We then find the L.C.M by dividing the numbers which is a factor for more than 1 of the given numbers. We then multiply the numbers that were obtained after performing the division process to find the required value of L.C.M.

Complete step-by-step answer:
According to the problem, we are asked to find the L.C.M (Least common multiple) of the numbers 64, 36 and 80.
We know that the L.C.M is defined as the smallest number that can be divided by all the given numbers.
Now, let us find the L.C.M of the numbers 64, 36 and 80.
$\begin{align}
  & 2\left| \!{\underline {\,
  64,36,80 \,}} \right. \\
 & 2\left| \!{\underline {\,
  32,18,40 \,}} \right. \\
 & 2\left| \!{\underline {\,
  16,9,20 \,}} \right. \\
 & 2\left| \!{\underline {\,
  8,9,10 \,}} \right. \\
 & \left| \!{\underline {\,
  4,9,5 \,}} \right. \\
\end{align}$.
Let us multiply all the numbers to find the L.C.M of the given numbers.
So, the L.C.M of the numbers is $2\times 2\times 2\times 2\times 4\times 9\times 5=2880$.
We have found the L.C.M of the numbers 64, 36 and 80 as 2880.

So, the correct answer is “Option (b)”.

Note: We can also solve the problem by dividing the product of the given numbers with the H.C.F (Highest Common Factor) of the given numbers. We should continue dividing the numbers in the L.C.M up to the point that we cannot have common factors for more than one number present. We should not make calculations correctly. Similarly, we can expect problems to find the H.C.F of the given numbers.