Lcm Worksheet questions with answers for class 5 are available in this post, student can practice from the question below. At the end of the post, LCM worksheets are provided with answers.

**LCM Questions for Class 5 with answers**

**1.Find the L.C.M. of the following by listing their multiples.**

**(i) 5, 10, 15**

The multipliers of 5 are: 5, 10, 15, 20, 25, 30, 35, . . .

The multipliers of 10 are: 10, 20, 30, 40, . . .

The multipliers of 15 are: 15, 30, 45, . . .

We can see that:

LCM( 5, 10, 15 ) = 30

**(ii) 4, 10, 12**

Write down multiples of each number until you find the first common multiple:

The multipliers of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, . . .

The multipliers of 9 are: 9, 18, 27, 36, 45, . . .

The multipliers of 12 are: 12, 24, 36, 48, . . .

We can see that:

LCM( 3, 9, 12 ) = 36

**(iii) 3, 9, 12**

Write down multiples of each number until you find the first common multiple:

The multipliers of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, . . .

The multipliers of 9 are: 9, 18, 27, 36, 45, . . .

The multipliers of 12 are: 12, 24, 36, 48, . . .

We can see that:

LCM( 3, 9, 12 ) = 36

**(iv) 2, 8, 10**

Write down multiples of each number until you find the first common multiple:

The multipliers of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, . . .

The multipliers of 8 are: 8, 16, 24, 32, 40, 48, . . .

The multipliers of 10 are: 10, 20, 30, 40, 50, . . .

We can see that:

LCM( 2, 8, 10 ) = 40

**(v) 7, 14, 21**

Write down multiples of each number until you find the first common multiple:

The multipliers of 7 are: 7, 14, 21, 28, 35, 42, 49, . . .

The multipliers of 14 are: 14, 28, 42, 56, . . .

The multipliers of 21 are: 21, 42, 63, . . .

We can see that:

LCM( 7, 14, 21 ) = 42

**(vi) 10, 20, 25**

Write down multiples of each number until you find the first common multiple:

The multipliers of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, . . .

The multipliers of 20 are: 20, 40, 60, 80, 100, 120, . . .

The multipliers of 25 are: 25, 50, 75, 100, 125, . . .

We can see that:

LCM( 10, 20, 25 ) = 100

**2. Find the L.C.M. of the following.**

(i) 60, 75, 120

lcm (60 75 120) =

60 => 2 x 2 x 3 x 5

75 => 3 x 5 x 5

120 => 2 x 2 x 2 x 3 x 5

= 2 x 2 x 3 x 5 x 5 x 2

= 600

lcm (60, 75 and 120) = 600

(ii) 48, 80, 112

lcm (48 80 112) = (?)

48 => 2 x 2 x 2 x 2 x 3

80 => 2 x 2 x 2 x 2 x 5

112 => 2 x 2 x 2 x 2 x 7

= 2 x 2 x 2 x 2 x 3 x 5 x 7

= 1680

lcm (48, 80 and 112) = 1680

(iii) 18, 54, 72

lcm (18 54 72) = (?)

18 => 2 x 3 x 3

54 => 2 x 3 x 3 x 3

72 => 2 x 2 x 2 x 3 x 3

= 2 x 3 x 3 x 3 x 2 x 2

= 216

lcm (18, 54 and 72) = 216

(iv) 10, 15, 25

LCM (10 15 25) = (?)

10 => 2 x 5

15 => 3 x 5

25 => 5 x 5

= 5 x 2 x 3 x 5

= 150

lcm (10, 15 and 25) = 150

(v) 20, 35, 45

lcm (20 35 45) = (?)

20 => 2 x 2 x 5

35 => 5 x 7

45 => 3 x 3 x 5

= 5 x 2 x 2 x 7 x 3 x 3

= 1260

lcm (20, 35 and 45) = 1260

(vi) 16, 24, 48

lcm (16 24 48) = (?)

16 => 2 x 2 x 2 x 2

24 => 2 x 2 x 2 x 3

48 => 2 x 2 x 2 x 2 x 3

= 2 x 2 x 2 x 2 x 3

= 48

lcm (16, 24 and 48) = 48

**3. Find the L.C.M. of the given numbers by division method.**

(i) 20 and 44

2 | 20 | 44 |

2 | 10 | 22 |

5 | 5 | 11 |

11 | 1 | 11 |

1 | 1 |

=2 * 2 * 5 * 11

LCM = **220**

(ii) 36, 24 and 40

2 | 24 | 36 | 40 |

2 | 12 | 18 | 20 |

2 | 6 | 9 | 10 |

3 | 3 | 9 | 5 |

3 | 1 | 3 | 5 |

5 | 1 | 1 | 5 |

1 | 1 | 1 |

2 * 2 * 2 * 3 * 3 * 5

LCM = **360**

(iii) 45 and 120

Step 1 :

2 | 45 | 120 |

2 | 45 | 60 |

2 | 45 | 30 |

3 | 45 | 15 |

3 | 15 | 5 |

5 | 5 | 5 |

1 | 1 |

Step 2: 2 * 2 * 2 * 3 * 3 * 5

Step 3 : LCM = **360**

(iv) 84 and 90

Step 1

2 | 84 | 90 |

2 | 42 | 45 |

3 | 21 | 45 |

3 | 7 | 15 |

5 | 7 | 5 |

7 | 7 | 1 |

1 | 1 |

Step 2: 2 * 2 * 3 * 3 * 5 * 7

Step 3: LCM = **1260**

(v) 10, 15 and 45

Step 1:

2 | 10 | 15 | 45 |

3 | 5 | 15 | 45 |

3 | 5 | 5 | 15 |

5 | 5 | 5 | 5 |

1 | 1 | 1 |

Step 2 : 2 * 3 * 3 * 5

Step 3 : LCM = **90**

(vi) 70, 110, 150

Step 1

2 | 70 | 110 | 150 |

3 | 35 | 55 | 75 |

5 | 35 | 55 | 25 |

5 | 7 | 11 | 5 |

7 | 7 | 11 | 1 |

11 | 1 | 11 | 1 |

1 | 1 | 1 |

Step 2 : 2 * 3 * 5 * 5 * 7 * 11

Step 3 : LCM = **11550**

(vii) 25, 30, 150

Step 1

2 | 25 | 30 | 150 |

3 | 25 | 15 | 75 |

5 | 25 | 5 | 25 |

5 | 5 | 1 | 5 |

1 | 1 | 1 |

Step 2 :2 * 3 * 5 * 5

Step 3 : LCM = **150**

(viii) 36, 60, 120

Step 1

2 | 36 | 60 | 120 |

2 | 18 | 30 | 60 |

2 | 9 | 15 | 30 |

3 | 9 | 15 | 15 |

3 | 3 | 5 | 5 |

5 | 1 | 5 | 5 |

1 | 1 | 1 |

Step 2 : 2 * 2 * 2 * 3 * 3 * 5

Step 3 :LCM = **360**

(ix) 30, 150, 300

Step 1

2 | 30 | 150 | 300 |

2 | 15 | 75 | 150 |

3 | 15 | 75 | 75 |

5 | 5 | 25 | 25 |

5 | 1 | 5 | 5 |

1 | 1 | 1 |

Step 2 : 2 * 2 * 3 * 5 * 5

Step 3 : LCM = **300**

(x) 25, 45, 105

Step 1

3 | 25 | 45 | 105 |

3 | 25 | 15 | 35 |

5 | 25 | 5 | 35 |

5 | 5 | 1 | 7 |

7 | 1 | 1 | 7 |

1 | 1 | 1 |

Step 2 :3 * 3 * 5 * 5 * 7

Step 3 : LCM = **1575**

(xi) 21, 49, 63

Step 1:

3 | 21 | 49 | 63 |

3 | 7 | 49 | 21 |

7 | 7 | 49 | 7 |

7 | 1 | 7 | 1 |

1 | 1 | 1 |

Step 2 : 3 * 3 * 7 * 7

Step 3 : LCM = **441**

**4. Solve the following:**

**(i) Find the lowest number which leaves 4 as remainder when divide by 9 and 12.**

Solution: LCM of two number is the lowest number divisible by the numbers . Let us find LCM of 9 and 12.

**Step 1 : **Write the given numbers in a horizontal line.

12 | 36 |

**Step 2 : **Divide the given numbers by smallest prime number. In this example we can divide by **2**.

(if any number is not divisible by **2**, write it down unchanged)

2 | 12 | 36 |

6 | 18 |

**Step 3 : **Continue dividing by prime numbers till we get 1 in all columns.

2 | 12 | 36 |

2 | 6 | 18 |

3 | 3 | 9 |

3 | 1 | 3 |

1 | 1 |

**Step 4 : **Multiply numbers in first column to get LCM.

**LCM( 12, 36 ) = 2 · 2 · 3 · 3 = 36 **.

Lowest number divisible 9 and 12 is 36. Adding 4 to 36 we get 40. Hence the required number is 40, which gives remainder 4 when divided by 9 and 12.

**(ii) Find the lowest number which being increased by 3 is exactly divided by 8, 12 and 16.**

LCM of two number is the lowest number divisible by the numbers .

First Lets calculate LCM of **8,12,16**

** STEP **:

**1**Write down all of the numbers as a product of their prime factors:

• Prime factorisation of 8: 2 * 2 * 2 = 2^{3}

• Prime factorisation of 12: 2 * 2 * 3 = 2^{2} * 3^{1}

• Prime factorisation of 16: 2 * 2 * 2 * 2 = 2^{4}

** STEP **:

**2**Find highest power of each prime number: 2

^{4}, 3

^{1}

**STEP :3** Multiply these values together: 2^{4} * 3^{1} = 48

Lowest number divisible 8, 12 and 16 is 48. Subtracting 3 from 48 we get 45. Hence the required number is 45 , when 3 is added to 45 it is divided by 8 ,12 and 16.

**(iii) Find the lowest number which is less by 5 to be divided by 15, 25 and 50 exactly.**

Given the numbers are 15, 25 and 50.

Now to find the LCM we will use the prime factorization method. **#1** Write down all of the numbers as a product of their prime factors:

• Prime factorisation of 15: 3 * 5 = 3^{1} * 5^{1}

• Prime factorisation of 25: 5 * 5 = 5^{2}

• Prime factorisation of 50: 2 * 5 * 5 = 2^{1} * 5^{2}

**#2** Find highest power of each prime number: 3^{1} , 5^{2} , 2^{1}

**#3** Multiply these values together: 3^{1} * 5^{2} * 2^{1} = 150

Thus, **LCM(15,25,50) = 150**

But we know that the condition is the number when less by 5 will be divisible by 15, 25 and 50. Thus we will add 5 to this number. So the required number is 150+5=**155 **

So that when we remove 5 from 155 we get 150 and it is divisible by 15, 25 and 50.

Thus the answer is 155.

**(iv) Find the lowest number which is less by 2 to be divided by 56 and 98 exactly.**

Lets find out LCM of two **56** and **98 **number by prime factorization

**STEP: 1** Write down all of the numbers as a product of their prime factors:

• Prime factorisation of 56: 2 * 2 * 2 * 7 = 2^{3} * 7^{1}

• Prime factorisation of 98: 2 * 7 * 7 = 2^{1} * 7^{2}

** STEP:2** Find highest power of each prime number: 2

^{3}, 7

^{2}

**STEP:****3** Multiply these values together: 2^{3} * 7^{2} = 392

Thus, **LCM(56,98) = 392**

As Per the Question provided N + 2 = 392

=> N = 390 Lowest number is 390 which is less by 2 to be divided by 56 and 98 exactly

**(v) Find the lowest number which is more by 7 to be divided by 20, 50 and 100 exactly.**

**(vi) The product of the L.C.M. and H.C.F. of two numbers is 80. If one of the numbers is 20, find the other number.**

**(vii) Find the lowest number which is less by 9 to be divided by 21, 35 and 49 exactly.**

**(viii) The product of two numbers is 192. If the H.C.F. of the numbers is 4, find their L.C.M.**

**(ix) The H.C.F. two numbers is 6 and their L.C.M. is 36. If one of the numbers is 18, find the other number.**

**(x) The product of the H.C.F. and L.C.M. of two numbers is 1050. Find the product of numbers.**

**(xi) The product of two numbers is 144. If the L.C.M. of these numbers is 12, find their H.C.F.**

**(xii) The product of two numbers is 169. If the L.C.M. of these numbers is 13, find their H.C.F.**