Question

The L.C.M of the smallest 2 digit composite number and the smallest composite number is:
(a) 12
(b) 4
(c) 20
(d) 44

Answer 1

Hint:Composite number is a positive integer which has at least one divisor apart from 1 and the number itself so the smallest 2 digit composite number is 10 and the smallest composite number is 4 and find the L.C.M of these two numbers.

Complete step-by-step answer:
Composite numbers are the positive integers which have divisors other than 1 and the number itself.
For e.g. 6 is a composite number. The divisors of 6 are 1, 2, 3 and 6. So, the number 6 has divisors 2 and 3 which are apart from 1 and 6 (number itself).
The smallest 2 digit composite number is 10. The smallest 2 digit positive integer in a number system is 10. The divisors of 10 are 1, 2, 5 and 10. From the divisors, it is clearly visible that 10 is a composite number.
The smallest composite number is 4. The positive integers start from 1. 1 has a divisor only 1 so it is not a composite number. 2 is a positive integer after 1 and number 2 has divisors 1 and 2 so this is also not a composite number then number 3, it has divisors 1 and 3. Then 4, the divisors of 4 are 1, 2, 4 so this is a composite number and hence, 4 is the smallest composite number.
Now, we are going to find the L.C.M of the smallest 2 digit composite number and the smallest composite number.
The smallest 2 digit composite number is 10 and the smallest composite number is 4.
Taking L.C.M of the above two numbers we get,
L.C.M of (4, 10) is as follows:
The factors of:
4 = 1×2×2
10 = 1×2×5
L.C.M is the least common multiple and so from the factors of 4 and 10 we can see that 2(underlined one) is common among 4 and 10 and 2, 5 are the uncommon multiples so L.C.M (4, 10) is 2×2×5 or 20.
L.C.M (4, 10) = 20
Hence, the correct option is (c).

Note: Composite numbers are numbers which are not prime numbers. Prime number is a positive integer having divisors only 1 and the number itself.
1 is neither a prime nor a composite number.