Question

The LCM of smallest two digit composite number and smallest composite number is
A. 12
B. 4
C. 20
D. 44

Answer 1

Hint: Here, we will first find the two digit composite number and smallest composite number. Then we will find the factors of these two numbers using the factorization method. Then we will multiply each factor that has occurred for a maximum number of times to get the LCM of the numbers.

Complete step by step solution:
Composite numbers are the numbers which are having more than two factors.
We know that the smallest two digit number is 10 and is also a composite number and the smallest composite number is equal to 4.
So, the numbers are 4 and 10
Now we will find out the factors of the given numbers i.e. 4, 10.
Factors are the smallest numbers with which the given number is divisible and their product will give the original number.
The factors of the number 4 are \[2 \times 2\].
Similarly we will find the LCM of the other number i.e. 10.
Factors of the number 10 are \[2 \times 5\].
Now, to find out the LCM of the numbers we will take each factor with their maximum number of occurrences in a number i.e. factor 2 which occurs two times maximum and number 5 which occurs one times maximum.
Therefore, LCM of the numbers 4 and 10 \[ = 2 \times 2 \times 5 = 20\]

So, option C is the correct option.

Note:
Here we should note that LCM (Least Common Multiple) of the given numbers is the smallest number which is the multiple of the given numbers. HCF (Highest common factor) of the given numbers is the highest factor which is common in the given numbers. HCF of the numbers is generally less than or equal to the LCM of the number. Product of the LCM and the HCF of two numbers are equal to the product of the original numbers.