If two numbers are in ratio 12 ratio 7 and their LCM is 504 then find sum of numbers

The LCM of two numbers is 9 times their HCF. The sum of LCM and HCF is 500 . Find their HCF.

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10 Questions 10 Marks 7 Mins

Given:

Ratio of numbers = 7 ∶ 11

HCF = 28

Calculation:

Let the numbers be 7x and 11x

HCF of 7x and 11x is x

HCF = x = 28

The numbers will be 7 × 28 and 11 × 28

⇒ The numbers will be 196 and 308

Sum of numbers = 196 + 308

⇒ Sum of numbers = 504

∴ Sum of numbers is 504

Let the numbers be 7x and 11x.

Add the numbers:

⇒ 7x + 11x

⇒ 18x

Now see, the final number must be the factor of 18, so in options only 504 is multiple of 18.

∴ The sum of two number is 504.

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80 Questions 80 Marks 80 Mins

Given:

The sum and LCM of two numbers are 156 and 504.

Concept used:

HCF of two numbers.

Calculation:

Sum = 156, LCM = 504

156 = 12 × 13

504 = 12 × 42

HCF = 12

Two numbers are 12a, 12b

12a + 12b = 156

a + b = 13

LCM = 12ab

12ab = 504

ab = 42

∴ a = 6, b = 7

two numbers be 12a and 12b

two numbers are 72, 84

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