Question

find HCF and LCM of 112 and show that 112 × 86 = HCF ×LCM.​

Answer 1

Corrected Question:

Find the HCF and LCM of 112 and 86. Also Show that HCF×LCM = 112×86.

To Find:

• HCF and LCM of 112 and 86.

To Prove:

• HCF×LCM=112×86

Concept:

To Find the HCF and LCM of given numbers, we have to firstly find the Prime Factorisation of each. After finding the HCF and LCM of number s we have to prove that Product of HCF and LCM equals to Product of the numbers.

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Solution:

Let's find out the prime factors of 112.

>> Prime Factors of 112 = 2×2×2×2×7

>> Prime Factors of 112= 2⁴×7¹

Now,

>> Prime Factors of 86= 2×43

>> Prime Factors of 86=2¹×43¹

Here, the common factor of 112 and 86 is 2.

To Find the HCF, we list out the common prime factors and thier smalleat exponents. So,

$\rightarrow\mathsf{HCF=2}$

To Find the LCM, we list out all prime factors and their greatest exponent. So,

$\rightarrow\mathsf{LCM={2}^{4}\times 7\times 43}$

$\rightarrow\mathsf{LCM=4816}$

Required Answer:

HCF and LCM of 112 and 86 are 2 and 4816 respectively.

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Now, we have to prove that HCF×LCM=112×86

Let's take LHS first. So,

$\rightarrow\mathsf{LHS=HCF\times LCM=2\times 4816}$

$\rightarrow\mathsf{LHS=HCF\times LCM=9632}$

Now,

$\rightarrow\mathsf{RHS=112\times 86= 9632}$

Hence, LHS=RHS. That is,

$\sf{HCF\times LCM=112\times 86}$

Hence Proved !!

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More to Know:

• HCF stands for Highest Common Factors
• LCM stands for Least common multiple

Answer 2

Answer:

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Step-by-step explanation:

Determining HCF of Numbers 112,86 by Euclid's Division Lemma

So, follow the step by step explanation & check the answer for HCF(112,86). Notice that 2 = HCF(8,2) = HCF(26,8) = HCF(86,26) = HCF(112,86) . Therefore, HCF of 112,86 using Euclid's division lemma is 2.