Question

find the LCM and HCF of following pairs of integers and verify that HCF×LCM = product of the Integers 26 and 91


give me correct answer.​

Answer 1

Real numbers

HCM is the Highest common factor And LCM is the Least common multiple.

Prime factor of 26:

→ 2 × 13

Prime factor of 91:

→ 7 × 13

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LCM of 26 and 91:

→ 2 × 7 × 13 = 182

HCF of 26 and 91:

→ 13

Now, let's verify LCM × HCF = Product of numbers.

Substituting all the values in it, we get:

→ 182 × 13 = 26 × 91

→ 2366 = 26 × 91

→ 2366 = 2366

Here, both the condition satisfy, so our answer is correct.

Hence verified!

Answer 2

Answer:

Given :-

• The integers is 26 and 91

To Find :-

• What is the LCM and HCF of the following pairs and we have to verify that pairs.

Formula Used :-

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\pink{HCF \times LCM =\: Product\: Of\: The\: Integers}}}$

Solution :-

First, we have to find the prime factors of 26 and 91 :

❒ Prime Factor of 26 :

$\implies \sf Prime\: Factor =\: 26$

$\implies \sf\bold{\purple{Prime\: Factor =\: 2 \times 13}}$

❒ Prime Factor of 91 :

$\implies \sf Prime\: Factor =\: 91$

$\implies \sf\bold{\purple{Prime\: Factor =\: 7 \times 13}}$

Now, we have to find the LCM of 26 and 91 :

$\implies \sf 26 =\: 2 \times 13$

$\implies \sf 91 =\: 7 \times 13$

Then, the LCM is :

$\longrightarrow \sf 2 \times 13 \times 7$

$\longrightarrow \sf 26 \times 7$

$\longrightarrow \sf\bold{\red{182}}$

Now, we have to find the HCF of 26 and 91 :

$\implies \sf 26 =\: 2 \times 13$

$\implies \sf 91 =\: 7 \times 13$

Hence, the HCF is :

$\longrightarrow \sf\bold{\red{13}}$

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★ VERIFICATION ★

Given :

• HCF = 13
• LCM = 182
• First Integers = 26
• Second Integers = 91

According to the question by using the formula we get,

$\footnotesize\mapsto \sf\bold{\pink{HCF \times LCM =\: Product\: Of\: Two\: Integers}}$

$\leadsto \sf 13 \times 182 =\: 26 \times 91$

$\leadsto \bf 2366 =\: 2366$

Hence, Verified.

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✪ EXTRA INFORMATION ✪

✧ H.C.F (Highest Common Factor)

• H.C.F or Highest Common Factor is the largest common factor that two or more number have.

✧ L.C.M (Least Common Multiple)

• L C.M or Least Common Multiple of two or more number is the smallest number is that is a multiple of those numbers.