r19 wrote:
Bunuel wrote:
6. If the least common multiple of a positive integer x, 4^3 and 6^5 is 6^6. Then x can take how many values?
A. 1
B. 6
C. 7
D. 30
E. 36
We are given that\(6^6=2^{6}*3^{6}\) is the least common multiple of the following threenumbers:
x;
\(4^3=2^6\);
\(6^5 = 2^{5}*3^5\) ;
First notice that\(x\) cannot have any other primes other than 2 or/and 3 , because LCM contains only these primes.
Now, since the power of 3 in LCM is higher than the powers of 3 in either the second number or in the third,
A. 1
B. 6
C. 7
D. 30
E. 36
We are given that\(6^6=2^{6}*3^{6}\) is the least common multiple of the following threenumbers:
x;
\(4^3=2^6\);
\(6^5 = 2^{5}*3^5\) ;
First notice that\(x\) cannot have any other primes other than 2 or/and 3 , because LCM contains only these primes.
Now, since the power of 3 in LCM is higher than the powers of 3 in either the second number or in the third,
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