Question

How will you find the lowest common multiple (LCM) of 8 and 10.

Answer 1

Hint:
In this question, we will first find the prime factors of numbers 8 and 10 in exponential form. After finding the prime factors we will look for the highest exponential prime factors or the numbers with largest power of each factor and multiply them.

Complete step by step solution:
Firstly, we will find the prime factors of 8 in exponential form
\[8 = 2 \times 2 \times 2 = {2^3}\]

Now we will find the prime factors of 10 in exponential form
\[10 = 2 \times 5\]
Now, In order to find the lowest common multiple i.e. LCM, we will multiply the highest order prime number from each factor, we get
\[
  LCM = {2^3} \times 5 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\, = 2 \times 2 \times 2 \times 5 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\, = 40 \\
 \]

Hence, the lowest common multiple i.e. LCM of the given numbers 8 and 10 is 40.

Additional Information:
The Lowest Common Multiple i.e. LCM is also called as Least Common Multiple and Least Common Divisor (LCD). It is the smallest positive integer which is divisible by both the numbers whose LCM we are supposed to find. Least Common multiple can also be defined as the smallest positive number which is multiple of both the numbers whose LCM we have to find.

Note:
This question can be solved by a different method. In this method we have to find the Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) by any method you know.
HCF/GCD of 8 and 10 can be given as, \[HCF = 2\]
Now, multiply the given numbers and divide the product of the numbers by HCF
\[
  LCM = \dfrac{{8 \times 10}}{2} \\
  \,\,\,\,\,\,\,\,\,\,\, = \dfrac{{80}}{2} \\
  \,\,\,\,\,\,\,\,\,\,\, = 40 \\
 \]
Hence, LCM of the numbers 8 and 10 is 40.