Multiples math worksheet for identifying common multiples and listing numbers that fit specific criteria.

Let's solve this step-by-step.

---

Section A: Find the common multiple

We need to find a number that all the given numbers in each group are divisible by (i.e., they are all multiples of that number).

---

#### 1) Numbers: 8, 48, 36, 124, 84, 12, 16

Let’s check what these numbers have in common.

- All are even → divisible by 2
- Let’s see if they’re divisible by 4:
- 8 ÷ 4 = 2 ✔
- 48 ÷ 4 = 12 ✔
- 36 ÷ 4 = 9 ✔
- 124 ÷ 4 = 31 ✔
- 84 ÷ 4 = 21 ✔
- 12 ÷ 4 = 3 ✔
- 16 ÷ 4 = 4 ✔

All divisible by 4.
Now check if they’re divisible by higher numbers?

Try 8:
- 8 ÷ 8 = 1 ✔
- 48 ÷ 8 = 6 ✔
- 36 ÷ 8 = 4.5 ✘ → not divisible

So not all divisible by 8.

So 4 is the largest common factor? But wait — we're looking for a number such that all are multiples of it.

But let's test divisibility by 2 and 4, but can we go higher?

Wait — try divisibility by 12?
- 8 ÷ 12 → no → ✘

Try divisibility by 6?
- 8 ÷ 6 → no → ✘

Try divisibility by 4 again: all are divisible by 4? Yes!

But let’s check if there’s a common divisor greater than 4?

Check GCD of the set:
Let’s pick two numbers: 8 and 12 → GCD is 4
8 and 36 → GCD is 4
8 and 48 → 8
But 8 and 124 → GCD(8,124):
124 ÷ 8 = 15.5 → not divisible → so GCD less than 8

Actually, since 8 and 124:
124 ÷ 4 = 31 → yes
But 124 ÷ 8 = 15.5 → no

So not divisible by 8

Now check divisibility by 2: yes, all even

But we want the largest number that divides all.

Try divisibility by 4:
- 8 → yes
- 48 → yes
- 36 → yes (36 ÷ 4 = 9)
- 124 → 124 ÷ 4 = 31 → yes
- 84 → 84 ÷ 4 = 21 → yes
- 12 → 12 ÷ 4 = 3 → yes
- 16 → 16 ÷ 4 = 4 → yes

✔ All divisible by 4

Is any larger number dividing all? Try 6:
- 8 ÷ 6 → no → ✘

Try 12:
- 8 ÷ 12 → no → ✘

So 4 is the greatest common divisor? But the question says “All of these numbers are multiples of _______”

It doesn’t ask for the greatest — just a number that all are multiples of.

So possible answers: 1, 2, 4

But likely they want the greatest such number.

Let’s confirm:

- 8 = 4 × 2
- 48 = 4 × 12
- 36 = 4 × 9
- 124 = 4 × 31
- 84 = 4 × 21
- 12 = 4 × 3
- 16 = 4 × 4

✔ All divisible by 4

So answer: 4

---

#### 2) Numbers: 14, 21, 154, 63, 35, 84, 77

Look at these numbers.

Check divisibility by 7:
- 14 ÷ 7 = 2 ✔
- 21 ÷ 7 = 3 ✔
- 154 ÷ 7 = 22 ✔
- 63 ÷ 7 = 9 ✔
- 35 ÷ 7 = 5 ✔
- 84 ÷ 7 = 12 ✔
- 77 ÷ 7 = 11 ✔

All divisible by 7

Any larger? Try 14:
- 21 ÷ 14 = 1.5 → ✘

So 7 is the greatest common divisor.

Answer: 7

---

#### 3) Numbers: 81, 9, 27, 171, 108, 45, 36

Check divisibility by 9:
- 81 ÷ 9 = 9 ✔
- 9 ÷ 9 = 1 ✔
- 27 ÷ 9 = 3 ✔
- 171 ÷ 9 = 19 ✔
- 108 ÷ 9 = 12 ✔
- 45 ÷ 9 = 5 ✔
- 36 ÷ 9 = 4 ✔

All divisible by 9

Try 18?
- 81 ÷ 18 = 4.5 → ✘

Try 3? Yes, but 9 is better.

So answer: 9

---

✔ Section A Answers:

1) 4
2) 7
3) 9

---

Section B: From the list:

List:
1, 2, 15, 18, 24, 26, 28, 40, 42, 44, 60, 66, 88

Let’s go through each:

---

#### 1) A multiple of 3

A number divisible by 3 → sum of digits divisible by 3

Check:
- 1 → no
- 2 → no
- 15 → 1+5=6 → yes ✔
- 18 → 1+8=9 → yes ✔
- 24 → 2+4=6 → yes ✔
- 26 → 2+6=8 → no
- 28 → 2+8=10 → no
- 40 → 4+0=4 → no
- 42 → 4+2=6 → yes ✔
- 44 → 4+4=8 → no
- 60 → 6+0=6 → yes ✔
- 66 → 6+6=12 → yes ✔
- 88 → 8+8=16 → no

✔ Multiples of 3: 15, 18, 24, 42, 60, 66

---

#### 2) A multiple of 5

Ends in 0 or 5

- 1 → no
- 2 → no
- 15 → ends in 5 → ✔
- 18 → no
- 24 → no
- 26 → no
- 28 → no
- 40 → ends in 0 → ✔
- 42 → no
- 44 → no
- 60 → ends in 0 → ✔
- 66 → no
- 88 → no

✔ Multiples of 5: 15, 40, 60

---

#### 3) A multiple of 3 and 5

Must be divisible by both → divisible by LCM(3,5)=15

So from above, check which numbers are divisible by 15:

- 15 → 15 ÷ 15 = 1 → ✔
- 40 → 40 ÷ 15 = 2.66… → ✘
- 60 → 60 ÷ 15 = 4 → ✔

So: 15, 60

✔ Answer: 15, 60

---

#### 4) A multiple of 8

Check if divisible by 8 → last three digits divisible by 8 (but small numbers)

- 1 → no
- 2 → no
- 15 → no
- 18 → 18 ÷ 8 = 2.25 → no
- 24 → 24 ÷ 8 = 3 → ✔
- 26 → 26 ÷ 8 = 3.25 → no
- 28 → 28 ÷ 8 = 3.5 → no
- 40 → 40 ÷ 8 = 5 → ✔
- 42 → no
- 44 → 44 ÷ 8 = 5.5 → no
- 60 → 60 ÷ 8 = 7.5 → no
- 66 → no
- 88 → 88 ÷ 8 = 11 → ✔

✔ Multiples of 8: 24, 40, 88

---

#### 5) A multiple of 3 and 8

Must be divisible by LCM(3,8)=24

Check which numbers are divisible by 24:
- 24 → 24 ÷ 24 = 1 → ✔
- 48 → not in list
- 72 → not in list
- 96 → not in list

Only 24 in the list

✔ Answer: 24

---

#### 6) A multiple of 11

Check:
- 1 → no
- 2 → no
- 15 → no
- 18 → no
- 24 → no
- 26 → no
- 28 → no
- 40 → no
- 42 → no
- 44 → 44 ÷ 11 = 4 → ✔
- 60 → no
- 66 → 66 ÷ 11 = 6 → ✔
- 88 → 88 ÷ 11 = 8 → ✔

✔ Multiples of 11: 44, 66, 88

---

#### 7) A multiple of 8 and 11

LCM(8,11)=88

Check which numbers are divisible by 88:
- 88 → 88 ÷ 88 = 1 → ✔

Others?
- 176 → not in list

Only 88

✔ Answer: 88

---

✔ Final Answers:

---

Section A:

1) 4
2) 7
3) 9

---

Section B:

1) A multiple of 3: 15, 18, 24, 42, 60, 66
2) A multiple of 5: 15, 40, 60
3) A multiple of 3 and 5: 15, 60
4) A multiple of 8: 24, 40, 88
5) A multiple of 3 and 8: 24
6) A multiple of 11: 44, 66, 88
7) A multiple of 8 and 11: 88

---

✔ All solved! Let me know if you'd like this formatted as a printable answer sheet.