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# confude

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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.)

Feb 20, 2019

#1
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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.

Feb 20, 2019
#2
+4613
+3

The wording is a bit puzzling, but here's the take.

It has to be in form 15x+21y and a,b are integers, (not necessarily positive).

3 divides both the numbers, so 15x+21y needs to be a multiple of 3.

15a+21y=3

3?

Feb 20, 2019