Question

Which is the smallest whole number that can be represented as a sum of 3, 5 and 7 consecutive whole numbers?

Answer 1

Answer: 105

Your question: Which is the smallest whole number that can be represented as a sum of 3, 5 and 7 consecutive whole numbers?

Step-by-step explanation:

Let x be the smallest whole number that can be represented as a sum of 3, 5 and 7 consecutive whole numbers.

Let (a-1), a and (a+1) be the 3 consecutive numbers

Thus, (a-1)+a+(a+1)=x

This implies, 3a=x

Let (b-2), (b-1), b, (b+1) and (b+2) be the 5 consecutive numbers

Thus, (b-2)+ (b-1)+ b+ (b+1) +(b+2)=x

This implies, 5b=x

Let (c-3), (c-2), (c-1), c, (c+1), (c+2) and (c+3) be the 7 consecutive numbers

Thus, (c-3)+(c-2)+(c-1)+c+ (c+1)+(c+2)+ (c+3)=x

This implies, 7c=x

Thus, x is a multiple of 3,5 and 7.

Least common multiple of 3,5, 7=105

Hence, 105 is the smallest whole number that can be represented as a sum of 3( 34,35,36), 5(19,20,21,22,23) and 7(12,13,14,15,16,17,18) consecutive numbers.