Carcass wrote:
If the greatest common divisor of 51 and 288 is 3, what is the least positive common multiple of 51 and 288?
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There's a nice rule that says:
(greatest common divisor of x and y)(least common multiple of x and y) = xyExample: x = 10 and y = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above
rule, since (5)(30) = (10)(15)
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In this question, we can write:
(greatest common divisor of 51 and 288)(least common multiple of 51 and 288) = (51)(288)We're told that the greatest common divisor of 51 and 288 is 3.
So, we get:
(3)(least common multiple of 51 and 288) = (51)(288)Divide both sides of the equation by 3 to get:
least common multiple of 51 and 288 = (51)(288)/3 = 4896Answer: 4896