Question

Sum of H.C.F. and L.C.M of 4, 20 and 28 is
A) 140
B) 144
C) 74
D) 81

Answer 1

Hint: Here first we will find the factors of each of the given numbers using the prime factorization method and then find the HCF i.e. the common factor of three of the numbers and also the LCM i.e. the product of all the factors such that the common factor to three of the numbers is multiplied once and then add them to get the desired answer.

Complete step by step answer:
The given numbers are: - 4, 20, 28
We will first calculate the factors of each of the numbers using the prime factorization method.
The factors of 4 are:-
\[\Rightarrow 4 = 2 \times 2\]
Factors of 20 are:-
\[\Rightarrow 20 = 5 \times 2 \times 2\]
Factors of 28:-
\[\Rightarrow 28 = 7 \times 2 \times 2\]
Now we know that HCF is the highest common factor of three of the numbers
Hence, HCF of these numbers is:-
\[\Rightarrow H.C.F = 2 \times 2\]
\[\Rightarrow H.C.F = 4\]………………. (1)
Now we know that L.C.M is the least common factor of three of the numbers.
Hence, LCM of the three numbers is:-
\[\Rightarrow L.C.M = 5 \times 2 \times 2 \times 7\]
\[\Rightarrow L.C.M = 140\]……………………. (2)
Now adding the values in equation 1 and 2 we get:-
\[\Rightarrow H.C.F + L.C.M = 4 + 140\]
Simplifying it we get:-
\[\Rightarrow H.C.F + L.C.M = 144\]

Hence, option B is the correct option.

Note:
Students should note that we need to factorize the numbers into prime factors in order to get the correct HCF and LCM of the given numbers.
Also, in LCM we need to multiply the common factors only once with all other non-common factors.