Question

1. Can two numbers have 12 as their HCF and 234 as
their LCM? Give reasons to justify your answer.​

Answer 1

Answer:

NO

Step-by-step explanation:

Concept= HCF and LCM

Given= HCF and LCM

To find= Can the HCF and LCM given be of two numbers

Explanation=

The full form of HCF is Highest Common Factor.

The full form of LCM is Least Common Multiple.

We know that HCF of two numbers is the greatest Common Factor which can divide both the numbers.

Whereas the LCM is the common multiple of both the numbers.

Now, if HCF can divide both the numbers and LCM is also a multiple of both the number. Therefore, Both the numbers divide the LCM and Since HCF can also divide both the numbers which already implies that HCF will Divide the LCM of these numbers.

So,

HCF = 12

LCM= 234

We know that HCF will divide LCM so we proceed,

234/12= 19.5

Here HCF is not Dividing the LCM.

So, 12 and 234 can not be the HCF and LCM of two numbers together.

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