Question

the HCF and LCM of two numbers are 12 and 5040 , respectively . if one of the numbers is 144 , find the other number?​

Answer 1

Given

HCF=12,LCM=5040

and also one number is 144

Let the other number be x

As we know that

Product of two numbers is HCF×LCM

⟹144×x=12×5040

⟹x=420

Hence

$The \: \: other \: \: number \: \: is \: \: \: 420$

Answer 2

$\bold{ \pmb{GIVEN}} \\ \red{ \tt HCF \: of \: two \: numbers} = 12 \\ \tt \red{ \: LCM \: of \: two \: number} = 5040 \\ \tt \red{ \: One \: number }= 144 \\ \\ \\ \bold{\pmb{TO \: \: FINd}} \\ \bf{ \: Other \: number} \\ \\ \\ \bold{ \pmb{SOLUTION}} \\ \\ \small{\boxed{\mathbb{LCM \times HCF = PRODUCT \: OF \: TWO \: NUMBERS}}} \\ \\ \sf \: Let \: the \: other \: number \: be \: b \\ \rm 12 \times 5040 = 144 \times b \\ \rm 60480 = 144b \\ \rm \: b = \dfrac{60480}{144} \\ \\ \boxed{\bold {\pmb{\blue{\underline{ \dag \: \: Other \: \: number = 420}}}}}$