RELATIONSHIP BETWEEN HCF AND LCM WORKSHEET

1)  The LCM of two numbers is 432 and their HCF is 36. If one of the numbers is 108, then find the other number.

2)  The product of two numbers is 1320 and their HCF is 6. Find the LCM of the numbers. 

3)  Two numbers are in the ratio 2 : 3 and their HCF is 13. Find the LCM of those two numbers. 

4)  The LCM of two co-prime numbers is 5005. If one of the numbers is 65, then find the other number.

5)  If the product of two co-prime numbers is 117, find the LCM of the numbers. 

6)  The product of HCF and LCM of two positive numbers is 24 and the difference between them is 2. Find the numbers.  

Detailed Answer Key

Answer (1) :

Let x be the other number. 

We know that,

Product of the two numbers  =  LCM x HCF

Then, 

108(x)  =  432 x 36

Divide each side by 108.

x  =  (432 x 36) / 108

x  =  144

The other number is 144.

Answer (2) :

We know that,

LCM x HCF  =  Product of the two numbers

Substitute.  

LCM x 6  =  1320

Divide each side by 6.

LCM  =  220

Answer (3) :

Because the two numbers are in the ratio 2 : 3, the numbers can be assumed as 2x and 3x.

HCF (2x, 3x)  =  x

But, it is given that the HCF is 13.

Then, 

x  =  5

Substitute x = 13 in 2x and 3x.

2x  =  2(13)  =  26

3x  =  3(13)  =  39

So, the two numbers are 26 and 36.

We know that,

HCF x LCM  =  Product of the two numbers

Substitute.

13 x LCM  =  26 x 39

Divide each side by 13.

LCM  =  (26 x 39) / 13

LCM  =  78

Answer (4) :

Let x be the other number.

We know that,

Product of the two numbers  =  LCM x HCF

As the HCF of co-primes is 1,

65(x)  =  5005 x 1

65x  =  5005

Divide each side by 65.

x  =  77

The other number is 77.

Answer (5) :

Because the two numbers are co-prime, their HCF is 1. 

We know that,

LCM x HCF  =  Product of the two numbers 

Substitute. 

LCM x 1  =  117

LCM  =  117

Answer (6) :

Because the difference between the two numbers is 2, the numbers can be assumed as x and (x + 2).  

We know that,

Product of the two numbers  =  LCM x HCF

Substitute. 

x(x + 2)  =  24

x² + 2x  =  24

Subtract 24 from each side. 

x² + 2x - 24  =  0

Solve for x by factoring. 

x² - 4x + 6x - 24  =  0

x(x - 4) + 6(x - 4)  =  0

(x - 4)(x + 6)  =  0

x  =  4  or  x  =  -6

Because the numbers are positive x ≠ 6. 

Then, x = 4. 

The other number : 

x + 2  =  4 + 2  =  6

So, the two numbers are 4 and 6.

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