LCM — least common multiple

A multiple of 7 is found by multiplying 7 by any whole number: $7\times 1=7$, $7\times 2=14$, $7\times 3=21$, and so on.

List the multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, … We are looking for which answer option appears in this list.

$7\times 7=49$, so 49 is a multiple of 7. None of the other options (45, 51, 54) appear in the multiples of 7.

We need a number that divides evenly by 7, meaning no remainder.

$45÷7=6$ remainder $3$. Since there is a remainder, 45 is not a multiple of 7.

$51÷7=7$ remainder $2$, and $54÷7=7$ remainder $5$. Neither divides evenly, so both are eliminated.

$49÷7=7$ exactly, with no remainder. So 49 is a multiple of 7. ✓

Multiples of 9 are found by multiplying 9 by $1,2,3,4,5,\dots$

$9\times 1=9$, $9\times 2=18$, $9\times 3=27$, $9\times 4=36$, $9\times 5=45$.

The first five multiples of 9 are 9, 18, 27, 36, 45.

Multiples are produced by skip counting — each term increases by the same number (9 in this case).

This list contains powers of 3, not multiples of 9 found by skip counting. The gaps between terms are not equal, so this is not a multiples list.

This list increases by 10 each time, not by 9. These are not multiples of 9.

This list increases by 3 each time — these are multiples of 3, not of 9.

9, 18, 27, 36, 45 increases by 9 each time and starts at 9, confirming these are the first five multiples of 9. ✓