Question

1. If HCF and LCM of two numbers are 24 and 360 respectively and
one of these number is 120 then what will be second number:
(A 72
(C) 144
(B) 36
(D) None of these​

Answer 1

Answer:

option (A) 72 is correct.

Step-by-step

WE HAVE GIVEN ONE NUMBER IS 120.

LET SECOND NUMBER BE = X

NOW WE CHECK THE VALUE OF X BY PUTTING NUMBER GIVEN BELOW.

THEREFORE,   TAKING X = 72

SO WE GET HCF = 24 AND 360.

I HOPE YOU WILL UNDERSTAND.  DON'T FORGET TO LIKE AND RATE.

Answer 2

$\bf \: \underline{ Given }\: :$ ↴

$\sf \: The \: HCF \: and \: LCM \: of \: two \: numbers \: are \: 24 \: and \: 360.$

$\sf \: The \: first \: number \: is \: 120.$

$\bf \: \underline{To \: find }\: :$ ↴

$\sf \: We \: have \: to \: find \: the \: Second \: number.$

$\bf \star \: \underline{ So, \: Let's \: Start }\: \star$

$\sf \: \longrightarrow\: HCF \: of \: two \: numbers \: = \: 24$

$\sf \: \longrightarrow \: LCM \: of \: two \: numbers \: = \: 360$

$\sf \: \longrightarrow \: One \: of \: the \: number \: = \: 120$

$\rm \: \bold {As \: we \: know \: that, }$

$\boxed{ \purple{\sf \: LCM \: \times \: HCF \: = \: Product \: of \: two \: numbers. }}$

$\sf \: LCM \: \times \: HCF \: = \: First \: number \: \times \: Second \: number.$

$\sf \: \underline{ Putting \: the \: value \: into \: the \: formula}$

$\sf \: Let \: the \: second \: number \: be \: x.$

$\sf \: 360\: \times \: 24 \: = \: 120 \: \times \: x$

$\sf \: 8640 \: = \: 120 \: x$

$\sf \: x \: = \: \dfrac{8640}{120}$

$\large\sf \: x \: = \: 72$

$\green{ \sf \: So, \: the \: second \: number \: is \: 72. }$

$\sf \: Let's \: verify \: our \: answer :$ ↴

$\sf \: LCM \: \times \: HCF \: = \: First \: number \: \times \: Second \: number.$

$\sf \: 360\: \times \: 24 \: = \: \: 120 \times \: 72$

$\sf \: 8640 \: = \: 8640$

$\sf \: \underline{So, \: the \: Second \: number \: is \: 72. }$