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 = 23
• Prime factorisation of 12: 2 * 2 * 3 = 22 * 31
• Prime factorisation of 16: 2 * 2 * 2 * 2 = 24
STEP : 2 Find highest power of each prime number: 24 , 31
STEP :3 Multiply these values together: 24 * 31 = 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 = 31 * 51
• Prime factorisation of 25: 5 * 5 = 52
• Prime factorisation of 50: 2 * 5 * 5 = 21 * 52
#2 Find highest power of each prime number: 31 , 52 , 21
#3 Multiply these values together: 31 * 52 * 21 = 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 = 23 * 71
• Prime factorisation of 98: 2 * 7 * 7 = 21 * 72
STEP:2 Find highest power of each prime number: 23 , 72
STEP: 3 Multiply these values together: 23 * 72 = 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.