Question

The lcm and hcf of two numbers a and b are 420 and 14 respectively.how many ordered pairs (a,b) are possible

Answer 1

The product of HCF and LCM equals the product of the numbers.

$HCF*LCM=a*b$

In this case we are given LCM and HCF as 420 and 14

Applying the above rule here

$420*14=a*b$

ab=5880

Now let us express 5880 as a product of two factors as follows:

1       ×      5880

2 × 2940

3 × 1960

4 × 1470

5 × 1176

6 × 980

7 × 840

8 × 735

10 × 588      

12 × 490      

14 × 420      

15 × 392      

20 × 294      

21 × 280      

24 × 245      

28 × 210      

30 × 196      

35 × 168      

40 × 147      

42 × 140      

49 × 120      

56 × 105      

60 × 98      

70 × 84

Answer: So the only ordered pair which has lcm as 420 and hcf as 14 is (14,420).

Answer 2

Concept

LCM means very cheap factor. It means very cheap number which might divide both the numbers. HCF means highest factor. It means the very best number which might divide both the numbers.

Given

LCM=420, HCF=14

To find

Number of ordered pairs.

Explanation

One finding of the LCM and HCF of two numbers is that the merchandise of two numbers are going to be LCM*HCF.

Applying the above rule here

ab=5880

(1,5880),(2,2940),(3,1960),(4, 1470),(5,1176),(6,980),(7,840),(8,735),(10,588), (12,490), (14,420), (15,392) , (20,294) , (21,280), (24,245) , (28,210) ,(30, 196) ,( 35,168) ,(40,147) ,(42,140) ,(49,120),(56,105) ,(60,98) ,(70, 84).

Hence there are 24 such pairs.

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