The integer 6 is the product of two consecutive integers (6 = 2 × 3) and the product of three consecutive integers (6 = 1 × 2 × 3). What is the next integer greater than 6 that is both the product of two consecutive integers and the product of three consecutive integers? Pick:	A) 153	B) 210	C) 272	D) 336	E) 600
Since the question asks the lowest possible so let us start with 153:   Any number divisible by 6 would satisfy that.   153 - 17 x 9   210 - divisible by 6 so it will have the pair 1 x 2 x 3   ANSWER:210
<result>B</result>
The integer 6 is the product of two consecutive integers (6 = 2 × 3) and the product of three consecutive integers (6 = 1 × 2 × 3). What is the next integer greater than 6 that is both the product of two consecutive integers and the product of three consecutive integers?