Two whole numbers, A and B, have a least common multiple of 180 and a greatest common factor of 12. Which value could be the sum of Aand B?
a.27
b.63
c.81
d.96

Question

HighDog224 · Answer

As 12 is the GCD of two whole numbers, let the numbers be A = 12 x and B = 12 y , where x < y . As the multiplication of two numbers is equal to the product of their GCD and LCM, then according to the given information, 12 x × 12 y = 12 × 180 . Simplify the obtained equation. x y = 12 × 180 12 × 12 = 15 Now, the possible pairs of two whole numbers x and y such that x < y and x y = 15 may be 1 and 15 or 3 and 5. If x = 1 and y = 15 , then A is 12 × 1 = 12 and B is 12 × 15 = 180 . So, the sum of A and B is 12 + 180 = 192 . Also, if x = 3 and y = 5 , then A is 12 × 3 = 36 and B is 12 × 5 = 60 . So, the sum of A and B is 36 + 60 = 96 . Therefore, according to the given choices, the correct option is d .

lovergirl · Answer

@highdog224 wrote:

As 12 is the GCD of two whole numbers, let the numbers be A = 12 x and B = 12 y , where x < y . As the multiplication of two numbers is equal to the product of their GCD and LCM, then according to the given information, 12 x × 12 y = 12 × 180 . Simplify the obtained equation. x y = 12 × 180 12 × 12 = 15 Now, the possible pairs of two whole numbers x and y such that x < y and x y = 15 may be 1 and 15 or 3 and 5. If x = 1 and y = 15 , then A is 12 × 1 = 12 and B is 12 × 15 = 180 . So, the sum of A and B is 12 + 180 = 192 . Also, if x = 3 and y = 5 , then A is 12 × 3 = 36 and B is 12 × 5 = 60 . So, the sum of A and B is 36 + 60 = 96 . Therefore, according to the given choices, the correct option is d .

could u make it a little easer i dont understand

HighDog224 · Answer

@lovergirl wrote:

@highdog224 wrote:

As 12 is the GCD of two whole numbers, let the numbers be A = 12 x and B = 12 y , where x < y . As the multiplication of two numbers is equal to the product of their GCD and LCM, then according to the given information, 12 x × 12 y = 12 × 180 . Simplify the obtained equation. x y = 12 × 180 12 × 12 = 15 Now, the possible pairs of two whole numbers x and y such that x < y and x y = 15 may be 1 and 15 or 3 and 5. If x = 1 and y = 15 , then A is 12 × 1 = 12 and B is 12 × 15 = 180 . So, the sum of A and B is 12 + 180 = 192 . Also, if x = 3 and y = 5 , then A is 12 × 3 = 36 and B is 12 × 5 = 60 . So, the sum of A and B is 36 + 60 = 96 . Therefore, according to the given choices, the correct option is d .

could u make it a little easer i dont understand

Basiclly its d just do all the nesacry steps

HighDog224 · Answer

@lovergirl wrote:

@highdog224 wrote:

As 12 is the GCD of two whole numbers, let the numbers be A = 12 x and B = 12 y , where x < y . As the multiplication of two numbers is equal to the product of their GCD and LCM, then according to the given information, 12 x × 12 y = 12 × 180 . Simplify the obtained equation. x y = 12 × 180 12 × 12 = 15 Now, the possible pairs of two whole numbers x and y such that x < y and x y = 15 may be 1 and 15 or 3 and 5. If x = 1 and y = 15 , then A is 12 × 1 = 12 and B is 12 × 15 = 180 . So, the sum of A and B is 12 + 180 = 192 . Also, if x = 3 and y = 5 , then A is 12 × 3 = 36 and B is 12 × 5 = 60 . So, the sum of A and B is 36 + 60 = 96 . Therefore, according to the given choices, the correct option is d .

could u make it a little easer i dont understand

and dont be lazy with it

lovergirl · Answer

im not lazy i just dont understand smart talk