If A is set of positive multiple of 5 less than 200 and B is the set of positive multiple of 7 less than 200.How many numbers are in both set A and set B?

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Answer 1 · 2018-05-03T19:56:06

#5# numbers

#5# and #7# have no common factors.

this means that the lowest common multiple of the two numbers is their product, i.e. LCM#(5,7) = 5 * 7#

#= 35#

all positive numbers that are multiples of both #5# and #7# must also be multiples of #35#.

this means that the numbers in both set A and set B (multiples of #7# and #5# less than #200#) are multiples of #35# less than #200#.

the multiples of #35# less than #200# are:

#35, 70, 105, 140, 175#

these are #5# numbers.