What is the product of X and Y ?
1. The greatest common factor of X and Y is 15
2. The least common multiple of X and Y is 180
Source: Original
Product of X and Y
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This is a very straight-forward question.
It is a property of nos that
the product of two numbers is equal to the product of its GCD and LCM.
Let me prove it to you through this example..
GCD = 15
LCM = 180
GCD = 15
this means
X = 15x
Y = 15y
where x and y dont have any common divisors
LCM = 180
LCM is the product of distinct factors
LCM = 15xy
15xy = 180
xy = 12
X*Y = 15x*15y = 15*15*12
LCM*GCD = 15*180 = 15*15*12
X*Y = LCM*GCD
It is a property of nos that
the product of two numbers is equal to the product of its GCD and LCM.
Let me prove it to you through this example..
GCD = 15
LCM = 180
GCD = 15
this means
X = 15x
Y = 15y
where x and y dont have any common divisors
LCM = 180
LCM is the product of distinct factors
LCM = 15xy
15xy = 180
xy = 12
X*Y = 15x*15y = 15*15*12
LCM*GCD = 15*180 = 15*15*12
X*Y = LCM*GCD
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I like Rijul007's approach, here is another one. This is more on the intuitive side:chieftang wrote:What is the product of X and Y ?
1. The greatest common factor of X and Y is 15
2. The least common multiple of X and Y is 180
Source: Original
1. GCF = 15, the numbers could be 15, 30; 15,45 etc. Hence insufficient
2. LCM = 180 the numbers could be 2,180; 15,180 etc. hence insufficient
Combining 1 and 2. We know both the numbers should have 3 and 5 or GCF can not be 15, note there can not be any more common terms between the numbers or GCF > 15. Now 180 = (2^2)*(3^3)*5, we know the numbers have 3 and 5 and nothing else common. Hence, 2^2 has to go to one number the remaining 3 can go to either number. Thus the numbers could be:
15, 12*15 or
3^2*5, 4*15
In either case the product of the numbers is (2^2)*(3^3)(5^2)
Hope this is not very confusing
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https://www.beatthegmat.com/760-done-dea ... 66740.html