Question

Find two 2digit numbers which have gcd =6 and lcm =432

Answer 1

Hcf = 6

LCM = 432

Hcf * LCM = product of the two numbers

6*432= 2592

32 and 81 are two two digit numbers which have hcf as 6 and LCM as 432

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Answer 2

Required two digit numbers are 48 and 54

Solution:

Given that,

LCM = 432

GCD = 6

Let two numbers are x and y

Now ,

x =  6a and y = 6b

where a and b are relative prime numbers of each others

6ab =LCM of x and y

6ab = 432

ab = 72

Now, relative prime to each other are (1, 72) and (8, 9)

Thus, numbers may be:  (6a , 6b)

(6 , 432) and (48 , 54)

Hence, required two digit numbers are 48 and 54

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