Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = the product of the two numbers 26 and 91.

By Mandeep Kumar|Updated : May 24th, 2023

To find: LCM and HCF of 26 and 91 and verify that LCM × HCF = the product of the two numbers.

First, determine the prime factors of the provided pairs of integers in order to determine the LCM and HCF of the numbers. The next step is to get the product of the least power of each numerical common factor to get the LCM of the 26 and 91. Next, determine the product of each number's prime factor with the highest power which will be the HCF of 26 and 91.

Let us find out the LCM and HCF of 26 and 91 first by Prime Factorization.

26 = 2 × 13
91 = 7 × 13

So, the LCM (26, 91) = 2 × 7 × 13 = 182 and the HCF (26, 91) = 13.

Verification of LCM × HCF = Product of two numbers 26 & 91

We have to find the value of LCM × HCF first and then product of two numbers 26 and 91.

So, let's start with LCM × HCF first.

Above, we have determined the value of LCM = 182 and HCF = 13

LCM × HCF = 182 × 13 = 2366

Now, find the value of product of two numbers 26 and 91

So, 26 × 91 = 2366.

We have found that LCM × HCF = 2366 and 

product of two numbers = 2366.

Hence, it is verified that LCM × HCF = Product of Two Numbers.

Summary:

Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = the product of the two numbers 26 and 91.

LCM and HCF of 26 and 91 are 182 and 13 respectively. It can be determined by finding the prime factors of 26 and 9. Then, find the product of LCM and HCF, i.e. 182 and 13, and then find the product of 26 and 91 to verify that LCM × HCF = the product of the two numbers.

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