Question

The HCF and LCM of two numbers are 50 and 1200 respectively. If the first
number is divided by 7, the quotient is 21 and remainder is 3, find the other
number.

Answer 1

Step-by-step explanation:

Given :-

The HCF and LCM of two numbers are 50 and 1200 respectively.

The first number is divided by 7, the quotient is 21 and remainder is 3.

To find :-

The other number .

Solution :-

Given that

The HCF of two numbers = 50

The LCM of the two numbers = 1200

Given that

The first number is divided by 7, the quotient is 21 and remainder is 3.

so, it can be written as

The first number = 7×21+3

=> First number = 147+3

=> First number = 150

Since,

Dividend=Divisor×Quotient+Remainder

The first number = 150

Let a = 150

Let the second number be b

We know that

Product of LCM and HCF of two numbers = Product of the two numbers

=> LCM × HCF = a×b

=> 1200×50 = 150×b

=> 150×b = 1200×50

=> 150 b = 60000

=> b = 60000/150

=> b = 400

Therefore, the other number = 400

Answer :-

The other number is 400

Check :-

We have ,

First number = 150

Other number = 400

150 = 2×3×5×5

400 = 2×2×2×2×5×5

HCF (150,400) = 2×5×5 = 50

LCM (150,400) = 2×5×5×3×2×2×2 = 1200

We have, LCM = 1200 and HCF = 50

The product of LCM and HCF

= 1200×50 = 60000

The product of the two numbers

= 150×400 = 60000

Therefore, LCM × HCF = a×b

Verified the given relations in the given problem.

Used formulae:-

→ Product of LCM and HCF of two numbers = Product of the two numbers

→Dividend = (Divisor × Quotient) +Remainder

Answer 2

Answer:

Given :-

• The HCF and LCM of two numbers are 50 and 1200 respectively.
• The first number is divided by 7, the quotient is 21 and remainder is 3.

To Find :-

• What is the other number.

Solution :-

Let,

$\mapsto \bf HCF =\: 50$

$\mapsto \bf LCM =\: 1200$

First, we have to find the first number :

As we know that :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Dividend =\: (Divider \times Quotient) + Remainder}}}\: \: \: \bigstar$

Given :

• Divider = 7
• Quotient = 21
• Remainder = 3

According to the question by using the formula we get,

$\footnotesize \implies \bf 1^{st}\: Number =\: (Divider \times Quotient) + Remainder$

$\implies \sf 1^{st}\: Number =\: (7 \times 21) + 3$

$\implies \sf 1^{st}\: Number =\: 147 + 3$

$\implies \sf\bold{\purple{1^{st}\: Number =\: 150}}$

Hence, the first number is 150 .

As we get the first number is 150, so we have to find the other means second number.

Now, we have to find the other number :

Let,

$\implies \bf 1^{st}\: Number =\: 150$

$\implies \bf 2^{nd}\: Number =\: y$

As we know that :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{H.C.F \times L.C.M =\: 1^{st}\: Number \times 2^{nd}\: Number}}}\: \: \: \bigstar$

Given :

• H.C.F = 50
• L.C.M = 1200
• First Number = 150

According to the question by using the formula we get,

$\implies \sf 50 \times 1200 =\: 150 \times y$

$\implies \sf 60000 =\: 150y$

$\implies \sf \dfrac{\cancel{60000}}{\cancel{150}} =\: y$

$\implies \sf 400 =\: y$

$\implies \sf\bold{\red{y =\: 400}}$

$\therefore$ The other number or second number is 400 .