HCF and LCM of two number are 12 and 72,sum of the two number is 60 , then one of the two number will be
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The highest common factor is found by multiplying all the factors which appear in both lists: So the HCF of 60 and 72 is 2 × 2 × 3 which is 12. The lowest common multiple is found by multiplying all the factors which appear in either list: So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.
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Step-by-step explanation:
We have with us that: The HCF and LCM of two numbers are 12 and 72 respectively. We also have with us that: sum of the two numbers is 60. So, either x=24 or x=36.
Given, HCF=12, LCM=72
One number =x, Other number =60−x
∴ Product of the two numbers = HCF × LCM
⇒x(60−x)=12×72
⇒x² −60x+864=0
⇒x² −36x−24x+864=0
⇒x(x−36)−24(x−36)=0
⇒(x−36)(x−24)=0
⇒x=36 or 24
∴ One of the number is 24.
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