Question

Find the LCM and HCF of the following pairs of integers and verify that LCM×HCF=product of the two numbers. 26 and 91 purn Sar long metho

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Answer 1

Answer:

Step-by-step explanation:

(i) 26 = 2 x 13

91 = 7x13

HCF =13

LCM = 2 x 7 x 13 =182

Product of the two numbers = 26 x 91 = 2366

HCF X LCM = 13 x 182 = 2366

Hence, product of two numbers = HCF x LCM

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Answer 2

HCF = Highest Common Factor

LCM = Lowest Common Multiple

Now,

Two number (given)

26 and 91

To find:

The HCF and the LCM of both the given numbers (26 and 91) and verifying 'HCF×LCM = product of the two numbers'.

Now,

Prime factorization of both the number-

26 = 2 × 13

91 = 7 × 13

Now,

HCF(91,26) = 13

[Hint - select the common factor and take the lowest power.]

LCM(91,26) = 13 × 2 × 7 = 182

[Hint - Select the common factor and take the highest power and also multiply the remaining uncommon factors,]

Now,

Verifying

HCF × LCM = product of the two numbers

So,

LHS = 13 × 182 = 2366

And

RHS = 26 × 91 = 2366

Therefore,

LHS = RHS thus verified