Question

The HCF and LCM of two numbers are 13 and 833 respectively if one of the numbers is 119 . determine the other ​

Answer 1

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Answer 2

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Questions

maths - HCF

The product of HCF and LCM of two numbers is 119. Find the two numbers if one of the numbers is not 1. Please help me to solve this.

RIYA

Apr 8, 2014

Did you notice that

119 = 7 x 17 , that is, its only factors are prime numbers.

If we needed the HCF of

7 and 17 it would be 1

If we needed the LCM of

7 and 17 it would be 119

The product of 1 and 119 is 119

Our two numbers are 7 and 17

Further investigation:

suppose we have two numbers that have a common factor, e.g. 15 and 24

15 = 3x5

24 = 3x2x2x2

so LCF = 3

HCM = 3x5x8 = 120

product of 3 and 120 = 360

360 = 3x3x5x8 = 3^2 (5x8) which splits into 3x5 and 3x8

notice we have the square of the common factor times the other non-common factors

so our 119 = 1^2 (7x17)

which splits into 1x7 and 1x17

consider a product such as

5^2 (9x7) or 1575 as the product of the HCF and LCM

What were the two numbers?

According to the above, they would have been

5x9 and 5x7 or 45 and 35

check

for 45 and 35 , the HCF is 5

and the LCM = 5x9x7 or 315

then the product of the LCF and the HCM

is 5x315 = 1575