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k is a positive integer and 225 and 216 are both divisors of k. If k=(
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24 Jan 2022, 06:08
24 Jan 2022, 06:08
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k is a positive integer and 225 and 216 are both divisors of k. If k=(2^a)*(3^b)*(5^c), where a, b and c are positive integers, what is the least possible value of a+ b+ c?
A. 4
B. 5
C. 6
D. 7
E. 8
A. 4
B. 5
C. 6
D. 7
E. 8
Re: k is a positive integer and 225 and 216 are both divisors of k. If k=(
[#permalink]
24 Jan 2022, 19:51
24 Jan 2022, 19:51
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\(k > 0\) & divisible by \(225\) & \(216\)
\(k=(2^a)*(3^b)*(5^c)\)
We need to find the least value of \(a+b+c\)
For that, we need to find the \(lcm\) of \(225\) & \(216\)
\(225 = 5^2 * 3^2\)
\(216 = 2^3 * 3^3\)
\(LCM = 2^3 * 3^3 * 5^2\)
As \(k\) is divisible by \(225\) & \(216\), it will also be divisible by the \(lcm\) by which we can get the least sum of \(a + b + c\)
\(LCM = 2^3 * 3^3 * 5^2\) comparing with \(k=(2^a)*(3^b)*(5^c)\)
\(a = 3, b = 3, c = 2\)
The least sum of\( a + b + c = 8\)
Answer E
\(k=(2^a)*(3^b)*(5^c)\)
We need to find the least value of \(a+b+c\)
For that, we need to find the \(lcm\) of \(225\) & \(216\)
\(225 = 5^2 * 3^2\)
\(216 = 2^3 * 3^3\)
\(LCM = 2^3 * 3^3 * 5^2\)
As \(k\) is divisible by \(225\) & \(216\), it will also be divisible by the \(lcm\) by which we can get the least sum of \(a + b + c\)
\(LCM = 2^3 * 3^3 * 5^2\) comparing with \(k=(2^a)*(3^b)*(5^c)\)
\(a = 3, b = 3, c = 2\)
The least sum of\( a + b + c = 8\)
Answer E
gmatclubot
Re: k is a positive integer and 225 and 216 are both divisors of k. If k=( [#permalink]
24 Jan 2022, 19:51
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