If the product of two integers is 320 and their least common multiple is 80, what...
If the product of two integers is 320 and their least common multiple is 80, what is their greatest common divisor?
a) 2
b) 4
c) 5
d) 8
e) cannot be determined
Homework Answers
Let the 2 integers be a and b respectively. Since the product of two integers is 320, hence ab = 320. Further, since the least common multiple is 80, hence 80 is the smallest number which is divisible by both a and b. Also, the highest value of either a or, b is 80.
Further, 80 = 24 * 5 and 320 =26 * 5 . Since 5 is a factor of 80, one of the numbers a and b must be a multiple of 5 and the other number must be a multiple of 2. Also, 320/80 = 4.
With this analysis, it is apparent that the two numbers are 4 and 80. Their product is 320 and their least common multiple is 80.
The greatest common divisor of 4 and 80 is 4.
Option b) is the correct answer.
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