What is the smallest number which when increased by 3 is divisible by 12, 15, 35, and 40? Select the correct option
A) 837 B) 947 C) 1027 D) 1155 E) 1231

Rationale: "factor each of the numbers 8 , 15 , 35 , and 40 into primes : 12 = 2 * 2 * 3 ; 15 = 3 * 5 ; 35 = 5 * 7 ; 40 = 2 * 2 * 2 * 5 the smallest number divisible by all of them is thus 2 * 2 * 2 * 3 * 5 * 7 = 840 837 + 3 = 840 a"
Answer: A