Question

What is the LCM of 36, 8, 72, 12?

Answer 1

Hint: The given numbers are all even numbers. In order to find the LCM we will first find the factors of the given numbers. Then first we will take common factors and then the uncommon one. The product of these factors will be the LCM of the numbers above. This method will be the prime factors method.

Complete step-by-step answer:
Given that, four numbers are 36, 8, 72, 12.
Now we will write the numbers in the form of a product of prime numbers.
\[8 = 2 \times 2 \times 2\]
\[12 = 2 \times 2 \times 3\]
\[36 = 2 \times 2 \times 3 \times 3\]
\[72 = 2 \times 2 \times 2 \times 3 \times 3\]
Now the common factor is 2,2. Now the remaining factors will be 2,3,3.
Now the product of these common and uncommon factors will be the LCM of the numbers above.
Thus the product will be \[2 \times 2 \times 2 \times 3 \times 3 = 72\]
Thus we found the LCM.

Note: Note that, LCM is the lowest common multiple. We can find LCM in many other ways also. But we will preferably use the prime factorization method. This method only uses prime numbers in the factor form. Also note that, we can use a tabular method also to find the LCM that also uses prime numbers.