Problem
Numbers divisible by several are common multiples
Out of the numbers 18, 16, 24, and 21, we must find the single number that can be divided evenly (no remainder) by both 3 and 4.
Operations
Your answer
Watch out Don't stop after checking just one divisor — a number that passes the 4-test alone (like 16) isn't automatically the answer; it must also pass the 3-test.
How to solve
Strategy Eliminate Possibilities — There is a small, genuinely finite set of four numbers and two clear logic clues (divisible by 3, divisible by 4). Testing each clue lets us cross off numbers until one survives both.
1STEP 1
Keep only the multiples of 4
Among 18, 16, 24, 21, only 16 and 24 are multiples of 4 — 18 and 21 leave a remainder.
16 = 4 × 4, 24 = 4 × 6
Grade 3 times-tables: a number is divisible by 4 only if it appears in the 4 times table.
3.OA.C.7Eliminate Possibilities2STEP 2
Of those, keep the multiples of 3
Of 16 and 24, only 24 is a multiple of 3 (24 = 3 × 8) — 16 is eliminated.
24 = 3 × 8, 16 ≠ 3 × (whole number)
Grade 3 unknown-factor sense: 24 divided by 3 is 8 with nothing left over, so 24 is a multiple of 3.
3.OA.B.6Eliminate PossibilitiesOf the two numbers left after the divisible-by-4 test, only 24 is also divisible by 3, so 24 is the single number divisible by both 3 and 4.
Why?
24 is divisible by 3 because 24 is exactly 3 times 8, while 16 is not 3 times any whole number.
Why?
Saying 24 is 3 times 8 means 24 is made of 8 equal groups of 3 with nothing sticking out, so the 24 splits cleanly into threes.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Once 24 is 3 times 8, dividing 24 by 3 must give back 8 with a remainder of 0, because dividing reverses multiplying.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
24 already passed the divisible-by-4 test in the earlier step, so being divisible by 3 as well means 24 clears both clues at once.
Why?
24 is divisible by 4 because 24 is exactly 4 times 6, which is 6 equal groups of 4 with nothing left over.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Answer
24
Check 24 against both clues directly: 24 divided by 3 is 8 (exact) and 24 divided by 4 is 6 (exact). Both are whole numbers, so 24 genuinely meets both conditions, and it is the only survivor.
Takeaway
Divisible by both 3 and 4 just means it shows up in both times tables, and 24 is the one that does!
- Keep only the multiples of 4
- Of those, keep the multiples of 3
Where next?
Another one like thissuggested
Step back and solidifysuggested