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What is the least common multiple of 3, 4x, 5y, 6xy, and 10y
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15 Dec 2019, 02:16
15 Dec 2019, 02:16
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100% (01:24) correct
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What is the least common multiple of 3, 4x, 5y, 6xy, and 10y?
A.60xy
B.30x2y2
C.25xy
D.30xy
E.60x2y2
A.60xy
B.30x2y2
C.25xy
D.30xy
E.60x2y2
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
What is the least common multiple of 3, 4x, 5y, 6xy, and 10y
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02 Jan 2020, 07:43
02 Jan 2020, 07:43
1
Lets solve it using two methods
Method 1:
Write all numbers as powers of prime numbers and other variables (in this case x and y)
3 -> 3^1
4x -> 2^2 * x
5y -> 5^1 * y
6xy -> 2^1 * 3^1 * x* y
10y -> 2^1 * 5^1 * y
Write down all unique prime numbers and variables (x,y in this case) which are present in at least one of the above numbers
2 * 3 * 5 * x* y
Take the maximum power of the unique prime numbers and variables, which are present in any of the numbers, in the factorization done above
2^2 * 3^1 * 5^1 * x^1 * y^1 = 4*3*5*xy = 60xy
Method 2:
Write numbers next to each other and at each stage divide by the number which is common in at least one of them. Example: First row we are diving by 3 as it is common in 3 and 6xy. If a number is not divisible by 3 then we write the number as it is in the next row.
Continue doing this till you get all numbers as 1 or if there are no common factors in all of the remaining numbers.
Multiply all the common factors and all the non common factors as shown in the figure to get the LCM
LCM = 3 * 2 * 5 * x * y * 2 = 60xy
So, Answer will be A
Hope it helps!
To learn more about LCM and GCD watch the following videos
Method 1:
Write all numbers as powers of prime numbers and other variables (in this case x and y)
3 -> 3^1
4x -> 2^2 * x
5y -> 5^1 * y
6xy -> 2^1 * 3^1 * x* y
10y -> 2^1 * 5^1 * y
Write down all unique prime numbers and variables (x,y in this case) which are present in at least one of the above numbers
2 * 3 * 5 * x* y
Take the maximum power of the unique prime numbers and variables, which are present in any of the numbers, in the factorization done above
2^2 * 3^1 * 5^1 * x^1 * y^1 = 4*3*5*xy = 60xy
Method 2:
Write numbers next to each other and at each stage divide by the number which is common in at least one of them. Example: First row we are diving by 3 as it is common in 3 and 6xy. If a number is not divisible by 3 then we write the number as it is in the next row.
Continue doing this till you get all numbers as 1 or if there are no common factors in all of the remaining numbers.
Multiply all the common factors and all the non common factors as shown in the figure to get the LCM
LCM = 3 * 2 * 5 * x * y * 2 = 60xy
So, Answer will be A
Hope it helps!
To learn more about LCM and GCD watch the following videos
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What is the least common multiple of 3, 4x, 5y, 6xy, and 10y [#permalink]
02 Jan 2020, 07:43
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