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
Shortcut Trick Note that the sum of two numbers is asked.
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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