a number has 2 and 5 as its prime factors what are the three smallest values
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The smallest number (positive integer) which has prime factors 2, 3 and 7 is 2*3*7 = 42. A positive integer N has prime factors 2, 3 and 7 if and only if it is a positive integral multiple of 42; i.e. if and only if there exists a positive integer k such that N = 42*k. So there are an infinite number of numbers which have the prime factors 2, 3 and 7. In order from lowest to highest the first ten such numbers are 42, 84, 126, 168, 210, 252, 294, 336, 378 and 420. The kth lowest such number is 42*k.
In general, the smallest number which has every number in a given set of prime numbers as factors is equal to the product P of that set of prime numbers, and a number N has every number in that set of prime numbers as a factor if and only if N is a positive integral multiple of P; i.e. if and only if there exists a positive integer k such that N = P*k......