Question

2) The HCF and LCM of two numbers are 12 and 360. If one of the number is 60 find the other
number​

Answer 1

GIVEN:

HCF of two numbers = 12

LCM of those two numbers = 360

One of the numbers = 60

TO FIND:

Another number

SOLUTION:

Let the other number be x

We know that,

Product of two numbers = HCF × LCM

According to the problem,

==> 60 × x = 12 × 360

==> x = (12 × 360) / 60

==> x = 12 × 6

==> x = 72

Therefore, the other number is 72.

Verification:

Product of two numbers = HCF × LCM

==> 60 × 72 = 12 × 360

==> 4320 = 4320

LHS = RHS

Hence, Verified!

Answer 2

GivEn:-

• HCF of two numbers:- 12
• LCM of two numbers:- 360
• One number:- 60

To Find:-

• Another number:- ?

Solution:-

★ $\bold{\underline{\underline{\boxed{\sf{\purple{HCF × LCM = First \; number(a) × Second \; number(b)}}}}}}$

:$\implies \sf {HCF × LCM = a × b}$

• 12 × 360 = 60 × b

• $\sf \dfrac{12 × 360}{60} = b$

• $\sf \dfrac{12 × \cancel{360}}{ \cancel{60}}$

• $\dag\large\bold{\underline{\underline{\boxed{\sf{\purple{72}}}}}}$

$\implies\large\bold{\underline{\underline{\sf{\pink{Hence, \; Another \; number \; is \; 72.}}}}}$

★ Verification:-

• HCF × LCM = a × b

• 12 × 360 = 60 × 72

• 4320 = 4320

$\implies \sf {LHS = RHS}$

$\implies\large\bold{\underline{\underline{\sf{\pink{Hence, \; Verified!}}}}}$

$\rule{100}{2}\rule{100}2}$