To find: the unknown integer. Given information: The GCF of 84 and another integer is 42, and their LCM is 252.

tinfoQ

tinfoQ

Answered question

2021-08-03

To find: the unknown integer.
Given information: The GCF of 84 and another integer is 42, and their LCM is 252.

Answer & Explanation

toroztatG

toroztatG

Skilled2021-08-04Added 98 answers

Calculation:
As per problem,
Let the other integer be x.
The GCF of 84 and x is 42, so x is a multiple of 42.
Their LCM is 252, so x is factor of 252.
The multiples of 42 which are also factors of 252 are 42,84, and 126.
Now, LCM and GCF of 84 and 84 is 84, so x is not equal to 84.
And, the LCM and GCF of 84 and 42 is 84, so x is also not equal to 84.
However, LCM and GCF of 84 and 126 is
84=242
126=342
LCM=2342=252
Therefore, x=126, that is, the other integer is 126.

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