For each of the following pairs, write a and b in standard form and use these factorizations to find (a, b) and [a, b]. a = 3780, b = 16,200

banganX

banganX

Answered question

2021-05-07

For each of the following pairs, write a and b in standard form and use these factorizations to find (a, b) and [a, b].
a = 3780, b = 16,200

Answer & Explanation

comentezq

comentezq

Skilled2021-05-08Added 106 answers

Step 1
Given :
a = 3780 and b = 16200.
To write a and b in standard form and to find (a, b) and [a,b].
Step 2
Standard form of n :
Suppose p1,p2,...,pr are the distinct prime factors of n arranged in order p1 then < ... < pr
n=p1m1p2m2...prmr where each mi is a positive integer.
(a, b) can be found by finding the product of all the common prime factors, with each common factor raised to the least power to which it appears in either factorization.
[a, b] can be found by finding the product of all distinct prime factors that appears in the standard form of either a or b, with each factor raised to the greatest power to which it appears in either factorization.
Step 3
Now,
a=3780=22×33×51×71
b=16200=23×34×52
Hence, the standard form of a and b are
a=3780=22×33×5×7
b=16200=23×34×52
Use these factorization to find (a, b) and [a,b]
(a,b)=(3780,16200)=22×33×5=540.
[a,b]=[3780,16200]=23×34×52×7=113400.
Hence, (a, b) = 540 and [a, b] = 113400.

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