What is the smallest positive integer that is the sum of a multiple of 15 and a multiple of 21? (Remember that multiples can be negative.)

ant101 Feb 20, 2019

#1**0 **

i not sure if it right

When we multiply odd and even numbers,

The product of an even number with any number is even.

The product of two odd numbers is odd.

Proofs by arrays can be used here, but they are unwieldy. Instead, we will use the previous results for adding odd and even numbers. Here are examples of the three cases:

6 × 4 = 24, 5 × 4 = 20, 7 × 3 = 21.

The first and second products are even because each can be written as the sum

of even numbers:

6 × 4 = 4 + 4 + 4 + 4 + 4 + 4 and 5 × 4 = 4 + 4 + 4 + 4 + 4.

The third product can be written as the sum of pairs of odd numbers, plus an extra

odd number:

7 × 3 = (3 + 3) + (3 + 3) + (3 + 3) + 3.

Each bracket is even, because it is the sum of two odd numbers, so the whole sum is odd.

bigbrotheprodude Feb 20, 2019