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

✬ Other Number = 420 ✬

Step-by-step explanation:

Given:

HCF and LCM of two numbers are 12 and 5040.

One number is 144.

To Find:

What is other number ?

Solution: Let the other number be x.

As we know that

★ Product of two numbers = (HCF)(LCM) ★

A/q

HCF = 12

LCM = 5040

One number = x

$\implies{\rm } x × 144 = 12 \times× 5040$

$\implies{\rm } 144x = 60480$

$\implies{\rm } x = 60480/144$

$\implies{\rm }⟹ x = 420$

Hence, the other number is x = 420

________________________

★ Verification ★

➟ Product of two numbers = HCF × LCM

$➟ 420 \times× 144 = 12 \times× 5040$

➟ 60,480 = 60,480

Answer 2

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