Question

The HCF and LCM of two number 23 and 828 when the first number is completed divided by 2 the quostient is 23. The other number is​

Answer 1

Answer:

other number is 64.

Step-by-step explanation:

Given :

HCF = 23

LCM = 828

Given :

When first number completely divided by 2 , the quotient is 23

let the first number is x

X/2 = 23

X = 23 x 2

X = 46

First number is 46

Product of two numbers = HCF x LCM

one number is 46.

let the second number is y.

46 * y = 23×128

46y = 2944

y = 2944÷46

y = 64

Secondnumber=64

Answer 2

SOLUTION

COMPLETE QUESTION

TO CHOOSE THE CORRECT OPTION

The HCF and LCM of two numbers are 23 and 828.When the first number is completely divided by 2 the quotient is 23. The other number is

(a) 420

(b) 410

(c) 414

(d) 425

CONCEPT TO BE IMPLEMENTED

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

EVALUATION

Here it is given that HCF and LCM of two numbers are 23 and 828.

Now first number is completely divided by 2 the quotient is 23

So we have

First number = 2 × 23 = 46

We know that

Product of two numbers = HCF × LCM

$\displaystyle \sf{ \implies 46 \times Second \: number = 23 \times 828}$

$\displaystyle \sf{ \implies Second \: number = \frac{23 \times 828}{46} }$

$\displaystyle \sf{ \implies Second \: number = \frac{828}{2} }$

$\displaystyle \sf{ \implies Second \: number = 414}$

FINAL ANSWER

Hence the correct option is (c) 414

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