Question

Find the L.C.M and H.C.F of 26 and 91 and verify that L.C.M $ \times $ H.C.F = product of two numbers.

Answer 1

Hint: In this question first factorize the number and calculate the value of L.C.M and H.C.F respectively by using the concept that the H.C.F of the numbers is the product of common factors, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
As we know that the H.C.F of the numbers is the product of common factors so, first factorize the numbers we have,

Factors of 26 is

$ \Rightarrow 26 = 1 \times 2 \times 13$

We cannot further factorize as 13 is a prime number.

Factors of 91 is

$ \Rightarrow 91 = 1 \times 7 \times 13$

We cannot further factorize as 13 is a prime number.

So the common factors of 26 and 91 are $\left( {1 \times 13} \right) = 13$

So the H.C.F of 26 and 91 is 13.

Now find out the L.C.M of 26 and 91,

Least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

So, the L.C.M of 26 and 91 is

$ \Rightarrow L.C.M = 1 \times 2 \times 7 \times 13 = 182$

So the product of L.C.M and H.C.F is $\left( {182 \times 13} \right) = 2366$.

And the product of two numbers is $\left( {26 \times 91} \right) = 2366$.

So, we verified that L.C.M $ \times $ H.C.F = product of two numbers.

So, this is the required answer.

Note: Whenever we face such types of questions the key concept is factorization so factorize the number and calculate L.C.M and H.C.F of the numbers respectively as above, then multiply L.C.M and H.C.F together and check that the product of two numbers is equal to the product of L.C.M and H.C.F if yes then it is verified.