Question

Q)If the sum of LCM and HCF of two numbers is 1300 and their LCM is 700 more than their HCF, then product of two numbers is 

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Answer 1

Answer:

700 = 2x2x5x5x7

1300 = 2x2x2x5x5x13

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Answer 2

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Let LCM = x and HCF = y

So, x + y = 1300 ......(1)

and x = y + 700 => x - y = 700 ......(2)

Adding equations 1 and 2 we get,

2x = 2000

=> x = 1000

Thus, y = x - 700 = 1000 - 700 = 300

So, LCM = 1000

HCF = 300

We know that for any two numbers a,b

HCF(a,b)×LCM(a,b) = a × b

Thus,

300 × 1000 = a × b

=> ab = 300000