If the greatest common factor of two integers is 28 and the least comm

Question

If the greatest common factor of two integers is 28 and the least common multiple is 840, what is the sum of the integers? 
 
(1) One of the integers is 168.
(2) One of the integers is 140.

rohit8865 · Answer

we need to know "The relation GCD(M, N) × LCM(M, N) = M × N"
let wo integers=M&N
thus 840*28=M*N

(1) we know value of one integer thus 2nd can be known
and thus their sum-------suff.
(2) we know value of one integer thus 2nd can be known
and thus their sum-------suff.

Ans D

Shiv2016 · Answer

Just plug in the values in the expression

LCM(x,y). HCF(x,y)= x.y

Its D

rhine29388 · Answer

We need to remember the golden rule :- Greatest common factor (x,y) * Least common multiple (x,y) = x * y
we are provided with values of GCF and LCM of both the numbers , using which we can obtain the product of 2 numbers x and y
If either of the number is mentioned then we can find other number very easily
In each of the statements one of the 2 numbers is mentioned which in turn can lead us to another number
So we finally obtain the value of sum of those number
Correct answer - D

pancakeprotein · Answer

For me what helped me tackle this was knowing the key insight and prime factorization.
Key Insight is GCF(a,b) * LCM(a,b) = a x b Now 28 * 840 = 23,520, however there is not much time to do that calculation. But putting in prime factorization is quick. 28 = 2^2 * 7 840 = 2^3 * 3 * 5 * 7 Together 28*840 = 2^5 * 3 * 5 * 7^2 Statement 1: Check if: 2^5 * 3 * 5 * 7^2 ] ------------------------- 2^3 * 3 * 7 ] divides cleanly into an integer. If yes, then statement 1 is sufficient. Do the process for statement 2, which in this case is also sufficient. Which gives to the final answer of D.

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