Question

The HCF AND LCM of two no.s are 48 and 288 respectively. one of the no.s is 144.Find the other no.​

Answer 1

Answer:

One number is 144. Let another number be x. It is given that HCF and LCM of two numbers are 48 and 288 respectively. Therefore the another number is 96.

Step-by-step explanation:

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Answer 2

• The other number = 96.

Given :

• The highest common factor (H.C.F.) = 48.
• The least common multiple (L.C.M.) = 288.
• One number = 144.

To Find :

• The other number.

Solution :

Let,

The other number be x.

We know that,

H.C.F. × L.C.M. = Product of two numbers

OR,

H.C.F. × L.C.M. = One number × Other number

We have,

• H.C.F. = 48.
• L.C.M. = 288.
• One number = 144.

$\implies \: \rm{48 \times 288 = 144 \times x }\\ \\ \implies \: \rm{13824 = 144x} \\ \\ \implies \: \rm{ \dfrac{13824}{144} = x } \\ \\ \implies \: \rm{96 = x} \\ \\ \implies \: \rm{x = 96}$

Hence,

The other number is 96.

Verification :

H.C.F. × L.C.M. = One number × Other number

Now we have,

• H.C.F. = 48.
• L.C.M. = 288.
• One number = 144.
• Other number = 96.

⇒ 48 × 288 = 144 × 96

⇒ 13824 = 13824

Hence Verified !!