There are two numbers. One of them is 84. Their Lowest Common Multiple (LCM) is 3780 and their Greatest Common Factor (GCF) is 12. What is the other number?

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Feb 12, 2018

Answer:

The other number is #540#

Explanation:

For any questions involving HCF and LCM,find each number as the product of the prime factors. That will tell you what you are working with.

#" "84 = color(blue)(2xx2xx3)xxcolor(red)(7)#
#" "? = ul(color(blue)(?xx?xx?)xx?xx?xx?xx?)#

#HCF = color(blue)(2xx2xx3) color(white)(wwwwwwwwwwwwww)= 12#
#LCM = color(blue)(2xx2xx3)xxcolor(red)(7)xxcolor(purple)(3xx3xx5)" " = 3780#

#3780 = color(blue)(HCF) xx color(red)(7) xx" another number"#
#3780 =" " color(blue)(12) xx color(red)(7)xxcolor(purple)((3xx3xx5))#
#3780 = " "color(blue)(12) xxcolor(red)(7) xxcolor(purple)(45)#

The other number cannot have #7# as a factor otherwise the #HCF# would be #84#

The other number is therefore #12 xx 45 =540#

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sjc Share
Feb 12, 2018

Answer:

#540#

Explanation:

we have

#hcf(84,b)=12#

#lcm(84,b)=3780#

to find #b#

we have the well known relationship

#ab=hcf(a,b)xxlcm(a,b)#

#84b=12xx3780#

#b=(cancel(12)xx3780)/cancel(84)^7#

#b=3780/7=540#

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Feb 12, 2018

Answer:

The second number would be the product of 45 and 12
540

Explanation:

Dividing 3780 by 84 gives one of the common factors of 84 and the second number.

# 3780/84 = 45 #

The HCF = 12 so the second number has factors of 45 and 12

# 45 xx 12 = 540#

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