Question

Find the HCF and LCM of 60, 32, 45, 80, 36 and 120.
$\left( A \right)$ 1, 1440
$\left( B \right)$ 2, 1440
$\left( C \right)$ 1, 480
$\left( D \right)$ 2, 480

Answer 1

Hint – In this particular question use the concept that first of all calculate all the prime factors of the given number for example the prime factors of 10 are (1, 2 and 5), prime factors are those which is divide by 1 or itself, and HCF of the two or more numbers is the multiplication of the common factors, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given numbers are 60, 32, 45, 80, 36 and 120.
As we know that the greatest common factor (G.C.F) or the highest common factor (H.C.F) is calculated by multiplying all the common factors of the given numbers.
So we have to first factories the polynomials and then take the common factors then multiplying these common factors together this factor is called the greatest common factor or the highest common factor (GCF/HCF) of the given polynomials.
And the LCM of any two numbers or more than two numbers is calculated as first list all the prime factors of each number, then multiply each factor the greatest number of times it occurs in the numbers. If the same factor occurs more than once in the given numbers then we have to multiply the factor the greatest number of times it occurs.
Therefore, first calculate the factors of the first number i.e. 60. So, the factors of 60 are,
$60 = 1 \times 2 \times 2 \times 3 \times 5$
Now calculate the factors of the second number i.e. 32. So, the factors of 32 are
$32 = 1 \times 2 \times 2 \times 2 \times 2 \times 2$
Similarly the factors of remaining numbers are
$45 = 1 \times 3 \times 3 \times 5$
$80 = 1 \times 2 \times 2 \times 2 \times 2 \times 5$
$36 = 1 \times 2 \times 2 \times 3 \times 3$
$120 = 1 \times 2 \times 2 \times 2 \times 3 \times 5$
Now as we see that the common factors of the given numbers is only 1.
So the required highest common factor (HCF) is = 1
And the L.C.M of the given numbers is
L.C.M = $1 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5$ = 1440
So the L.C.M is = 1440 and the H.C.F is = 1
So this is the required answer.
Hence option (A) is the correct answer.
Note – Whenever we face such types of questions the key concept we have to remember is that the LCM of two numbers or greater than two numbers is calculated as first list all the prime factors of each number, then multiply each factor the greatest number of times it occurs in the numbers. If the same factor occurs more than once in the given numbers then we have to multiply the factor the greatest number of times it occurs, so first find out the all the prime factors of each number as above then find out the LCM and HCF using the above written property as above calculated and then simplify we will get the required answer.