Question

LCM Of two number is 120 and their HCF is 12. if one no is 24, find the other number ?

Answer 1

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Answer 2

Answer:

Given :

Lowest common multiple ( LCM ( a,b ) ) = 120 .

Highest common factor ( HCF ( a,b ) ) = 12 .

One of the number is 24 .

We know that  : $\mathtt{Product\:of\:numbers=HCF\times LCM}$

Let the other number be x .

Hence :

$x\times 24 = 12\times 120\\\\\implies 24x=12\times 120\\\\\implies x=\dfrac{12\times 120}{24}\\\\\implies x=12\times 5\\\\\implies x=60$

The other number is 60 .

Verification :

HCF of 60 and 24

60 = 12 × 5

24 = 12 × 2

2 and 5 are coprime and hence 12 is the HCF .

LCM of 60 and 24

LCM of 60 and 24 will be :

60 = 12 × 5

24 = 12 × 2

LCM = 12 × 5 × 2

⇒ LCM = 120

Hence verified .