+249 If m is a 3-digit positive integer such that \(\mathop{\text{lcm}}[8m,10^{10}] = 4\cdot\mathop{\text{lcm}}[m,10^{10}]\), then what is the value of m?
The product of positive integers x, y and z equals 2004. What is the minimum possible value of the sum x+y+z?
+129841 The product of positive integers x, y and z equals 2004. What is the minimum possible value of the sum x+y+z?
The divisors of 2004 are 1 | 2 | 3 | 4 | 6 | 12 | 167 | 334 | 501 | 668 | 1002 | 2004
The minimum sum will come from the factors of the middle two divisors, 12 and 167
167 is prime....it will be included in the sum.......the divisors of 12 are 1 | 2 | 3 | 4 | 6 | 12.......
The remaining two integers involved in minimizing the sum will come from the middle two divisors of 12, i.e, 3 and 4
So....the minumum sum is given when the three integers x, y and z are 3 , 4 and 167 ....the sum = 174
+33653 "If m is a 3-digit positive integer such that , then what is the value of m?"
512
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