5th Grade Factors and Multiples Worksheets | L.C.M. | H.C.F. | Answers - Free Printable

Let’s go step by step through each problem on the worksheet.

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Top Section: Write the first three multiples of the given numbers.

Multiples are what you get when you multiply a number by 1, 2, 3, etc.

(i) For 4:
4 × 1 = 4
4 × 2 = 8
4 × 3 = 12
→ First three multiples: 4, 8, 12

(ii) For 7:
7 × 1 = 7
7 × 2 = 14
7 × 3 = 21
→ First three multiples: 7, 14, 21

(iii) For 13:
13 × 1 = 13
13 × 2 = 26
13 × 3 = 39
→ First three multiples: 13, 26, 39

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Question 1: Write the prime numbers between 11–30.

Prime numbers are numbers greater than 1 that have only two factors: 1 and themselves.

List numbers from 11 to 30:
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

Now pick the primes:

- 11 → prime (only divisible by 1 and 11)
- 12 → not prime (divisible by 2, 3, 4, 6)
- 13 → prime
- 14 → no
- 15 → no (divisible by 3, 5)
- 16 → no
- 17 → prime
- 18 → no
- 19 → prime
- 20 → no
- 21 → no (3×7)
- 22 → no
- 23 → prime
- 24 → no
- 25 → no (5×5)
- 26 → no
- 27 → no (3×9)
- 28 → no
- 29 → prime
- 30 → no

So prime numbers between 11 and 30:
11, 13, 17, 19, 23, 29

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Question 2: Find the common multiples of 2, 8 and 12.

Common multiples are numbers that all three divide into evenly.

First, find LCM (Least Common Multiple) of 2, 8, 12 — because any common multiple will be a multiple of the LCM.

Break them down:

- 2 = 2
- 8 = 2³
- 12 = 2² × 3

LCM takes highest powers: 2³ × 3 = 8 × 3 = 24

So common multiples are multiples of 24:
24, 48, 72, 96, ...

We can list a few:
24, 48, 72

(Any multiple of 24 is acceptable — we’ll give first three.)

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Question 3: Check the divisibility of given numbers.

(i) 86, 190 by 3

Rule for 3: Add digits. If sum is divisible by 3, then so is the number.

- 86: 8 + 6 = 14 → 14 ÷ 3 = 4.66… → Not divisible by 3
- 190: 1 + 9 + 0 = 10 → 10 ÷ 3 ≈ 3.33 → Not divisible by 3

Answer: Neither is divisible by 3.

(ii) 47, 815 by 3

- 47: 4 + 7 = 11 → 11 ÷ 3 ≈ 3.66 → Not divisible
- 815: 8 + 1 + 5 = 14 → 14 ÷ 3 ≈ 4.66 → Not divisible

Neither is divisible by 3.

Wait — let me double-check 815: 8+1+5=14 → yes, not divisible by 3.

But maybe I misread? Let me check again.

Actually, 815: 8+1+5=14 → correct. Not divisible.

But wait — perhaps the question meant “check if they ARE divisible” — so answer is “no” for both.

But let’s move on.

(iii) 2, 37, 405 by 11

Rule for 11: Alternating sum of digits. If result is 0 or divisible by 11, then yes.

- 2: single digit → not divisible by 11 (unless it's 0 or 11 itself) → No
- 37: 3 - 7 = -4 → not divisible by 11 → No
- 405: 4 - 0 + 5 = 9 → not divisible by 11 → No

None are divisible by 11.

Wait — 405: positions: hundreds=4, tens=0, units=5 → alternating: +4 -0 +5 = 9 → yes, not divisible.

(iv) 81, 620 by 4

Rule for 4: Last two digits form a number divisible by 4.

- 81: last two digits = 81 → 81 ÷ 4 = 20.25 → Not divisible
- 620: last two digits = 20 → 20 ÷ 4 = 5 → Yes! Divisible by 4

So: 81 → No; 620 → Yes

Summary for Q3:

(i) 86 → No, 190 → No
(ii) 47 → No, 815 → No
(iii) 2 → No, 37 → No, 405 → No
(iv) 81 → No, 620 → Yes

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Question 4: The LCM of 25 and 65 is 325. Find their HCF.

There’s a formula:
LCM × HCF = Product of the two numbers

So:
25 × 65 = ?
25 × 65 = 25 × (60 + 5) = 25×60 + 25×5 = 1500 + 125 = 1625

Given LCM = 325

So:
HCF = (25 × 65) / LCM = 1625 / 325

Calculate:
325 × 5 = 1625 → So HCF = 5

Check: Factors of 25: 1, 5, 25
Factors of 65: 1, 5, 13, 65
Common factor: 1, 5 → Highest is 5 → Correct.

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Question 5: The LCM of two numbers is 1344 and their HCF is 4. If one of the numbers is 84, find the other number.

Again, use:
LCM × HCF = Product of the two numbers

So:
1344 × 4 = 84 × ?
Left side: 1344 × 4 = 5376

So:
84 × x = 5376
x = 5376 ÷ 84

Let’s divide:

84 × 60 = 5040
5376 - 5040 = 336
84 × 4 = 336
So 60 + 4 = 64

Thus, x = 64

Check:
Is HCF of 84 and 64 equal to 4?
84 = 4 × 21
64 = 4 × 16
HCF of 21 and 16 is 1 → so overall HCF is 4 → Good.

LCM: LCM(84, 64) = (84 × 64)/4 = 5376/4 = 1344 → Matches.

Perfect.

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Final Answers:

Top section:
(i) 4, 8, 12
(ii) 7, 14, 21
(iii) 13, 26, 39

Q1: 11, 13, 17, 19, 23, 29
Q2: 24, 48, 72 (or any multiples of 24)
Q3:
(i) Neither divisible by 3
(ii) Neither divisible by 3
(iii) None divisible by 11
(iv) 81 → No, 620 → Yes
Q4: 5
Q5: 64

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Final Answer:
Top: (i) 4, 8, 12; (ii) 7, 14, 21; (iii) 13, 26, 39
1. 11, 13, 17, 19, 23, 29
2. 24, 48, 72
3. (i) No, No; (ii) No, No; (iii) No, No, No; (iv) No, Yes
4. 5
5. 64