3 Solved HCF And LCM Problems To Practice For SBI Exams

Dear Reader,
Below are four problems based on HCF and LCM calculations.

Question 1

Find the LCM of 1020 and 444

a) 10244 b) 37740 c) 12122 d) 18536

Answer : b)37740

Solution :

Remember that,
Product of two numbers = Product of their HCF and LCM
Here, 1020 x 444 = HCF x LCM
LCM = 1020 x 444 / HCF

i.e., first we have to find the HCF of 1020 and 444.
By using the method, "To find the HCF of two given numbers, divide the largest by the smallest number, then divide the dividend by the remainder. Repeat this until remainder is 0. The last dividend is the HCF of the two numbers."

1020 = 2 x 444 + 132
444 = 3 x 132 + 48
132 = 2 x 48 + 36
48 = 1 x 36 + 12
36 = 3 x 12 + 0
Therefore the last divident is 12.
Then the HCF of them is 12.

Now, LCM = 1020 x 444 / 12 = 37740.
Hence the required answer is 37740.

Question 2

Find the ratio of HCF and LCM of 1212 and 636.

a) 1:5353 b) 1:1212 c) 1:636 d) 1:7272

Answer : a)1:5353

Solution :

First, to find the HCF.
Given numbers are, 1212 and 636
1212 = 1 x 636 + 576
636 = 1 x 576 + 60
576 = 9 x 60 + 36
60 = 1 x 36 + 24
36 = 1 x 24 + 12
24 = 2 x 12 + 0
Then the HCF = 12.

And LCM = product of the numbers / HCF
LCM = 1212 x 636 / 12 = 1212 x 53
Now, the required ratio = HCF/LCM
12 / 1212 x 53 = 1/5353
Hence the ratio HCF: LCM = 1:5353

Question 3

The HCF of two numbers is 6 and their sum gives 102 then the numbers will be

(i) 24,78 (ii) 18,84 (iii) 54,48

a)(i) only b) i & ii only c) ii only d) i,ii & iii

Answer : d)i,ii & iii

Solution :

From the first option:(i) 24, 78
Then sum = 24+78 = 102
And the HCF of 24 and 78 = 6

From 2nd option (ii) 18,84
Then sum = 18+84 =102
And the HCF of 18 and 84 = 6

From 3rd option (iii) 54,48
Then sum = 54+48 =102
And the HCF of 54 and 48 = 6
Hence the answer is option d.


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