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

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

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

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

$\implies{\rm } x = 420$

Hence, the other number is x = 420

________________________

★ Verification ★

➟ Product of two numbers

$= HCF \times× LCM$

$➟ 420 \times× 144 = 12 \times× 5040$

➟ 60,480 = 60,480

Answer 2

$\Large\bold{\mathcal{\colorbox{yellow}{\blue{Solution:⤵}}}} \\ \large \bold{ \mathtt{ \colorbox{red}{ \blue{Given \: HCF=12,LCM=5040}}}} \\ \large \bold{ \mathcal{ \colorbox{pink}{ \pink{and also one number is 144}}}} \\ \large \bold{ \mathtt{ \colorbox{yellow}{ \blue{Let the other number be x}}}} \\ \large \bold { \mathtt{ \colorbox{orange}{{As we know that}}}} \\ \large \bold{ \mathtt{ \colorbox{navy}{ \orange{Product of two numbers is HCF×LCM}}}} \\ \large \bold{ \mathtt{ \colorbox{orange}{ \red{⟹144×x=12×5040}}}} \\ \large \bold{ \mathtt{ \colorbox{lime}{ \purple{⟹x=420}}}} \\ \large \bold{ \mathtt{ \colorbox{aqua}{ \red{So, The other number is 420}}}}$