What is the least common multiple of 4t to the power of 3 and 6t to the power of 4 ?

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1
Jan 20, 2018

Answer:

Please see the step process below;

Explanation:

Given;

#(4t)^3 = 4^3 t^3 = (4 xx 4 xx 4) (t xx t xx t) = 64t^3#

#(6t)^4 = 6^4 t^4 = (6 xx 6 xx 6 xx 6) (t xx t xx t xx t) = 1296t^4#

Hence looking for the LCM of both, we need to look for the factors of both as well..

Factor of #rArr 64t^3 = 2t xx 2t xx 2t xx 2 xx 2 xx 2#

Factor of #rArr 1296t^4 = 2t xx 2t xx 2t xx 2t xx 3 xx 3 xx 3 xx 3#

Now after finding the factors above, we look for their LCM.

Note: If both values have same factors, we choose only one of it..

For example;

Factor of #rArr x^4 = x xx x xx x xx x#

Factor of #rArr x^6 = x xx x xx x xx x xx x xx x#

Indentical ones are in color;

Factor of #rArr x^4 = color(blue)(x xx x xx x xx x)#

Factor of #rArr x^6 = color(blue)(x xx x xx x xx x )xx x xx x#

Hence the LCM of #x^4 and x^6 rArr color(blue)(x xx x xx x xx x) xx x xx x#
#color(white)(xxxxxxxxxxxxxxxxxxxxxxxxxx)darr#
[i.e. Taking the identical ones as a single factor, then adding the reminding factors that follows!]

Now back to our question!

We have the factors;

Factor of #rArr 64t^3 = 2t xx 2t xx 2t xx 2 xx 2 xx 2#

Factor of #rArr 1296t^4 = 2t xx 2t xx 2t xx 2t xx 3 xx 3 xx 3 xx 3#

Spotting out the identical factors;

Factor of #rArr 64t^3 = color(blue)(2t xx 2t xx 2t) xx 2 xx 2 xx 2#

Factor of #rArr 1296t^4 = color(blue)(2t xx 2t xx 2t) xx 2t xx 3 xx 3 xx 3 xx 3#

Therefore the LCM of #64t^3 and 1296t^4 rArr color(blue)(2t xx 2t xx 2t) xx 2t xx 2 xx 2 xx 2 xx 3 xx 3 xx 3 xx 3#

#color(white)(xxxxxxxxxxx) rArr 16t^4 xx 8 xx 81#

#color(white)(xxxxxxxxxxx) rArr 10, 368t^4#

Hope this helps!

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Write your answer here...
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Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

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Ujjwal Share
Jan 20, 2018

Answer:

See below

Explanation:

#4t^3 = 2*2*t*t*t#
#6t^4 = 2*3*t*t*t*t#

Thus,LCM = #2*2*3*t*t*t*t#
= #12t^4#

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