# What is the smallest number which when divided by 24 36 and 54 gives 5 as remainder each time?

Guys, does anyone know the answer?

get find the smallest number which when divided by 24, 30, 48, and 60 leaves a remainder 2 in each case from screen.

## What is the smallest number which when divided by 24, 36 and 54 gives a remainder of 5 each time?

Click here👆to get an answer to your question ✍️ What is the smallest number which when divided by 24, 36 and 54 gives a remainder of 5 each time?

Question

## What is the smallest number which when divided by 24,36 and 54 gives a remainder of 5 each time?

Hard Open in App Solution Verified by Toppr Let's factorize, 24 = 2x2x2x3 36 = 2x2x3x3 54 = 2x3x3x3

The smallest number divisible by all 24, 36, 54 is:

LCM(24, 36, 54) = 216

Thus, to get 5 as remainder, we need to add 5 to 216.

(as 216 is the smallest number which gives remainder 0 when divided by 24 or 36 or 54)

216 + 5 = 221

For 12, 221 gives 18 as quotient and 5 as remainder

For 36, 221 gives 6 as quotient and 5 as remainder

For 54, 221 gives 4 as quotient and 5 as remainder

Hence, 221 is required number.

96 22

स्रोत : www.toppr.com

## [Solved] Find the smallest number which when divided by 48 and 60, le

Given∶ A number when divided by 48 and 60, leaves a remainder 7 in each case. But when divided by 13 leaves no remainder. Formula Used∶ Concept of LCM a

Home Quantitative Aptitude Number System LCM and HCF LCM

13 14 15 11

Option 1 : 13

## Detailed Solution

Given

A number when divided by 48 and 60, leaves a remainder 7 in each case.

But when divided by 13 leaves no remainder.

Formula Used

Concept of LCM and Hit and Trial method

Calculation

LCM of 48 and 60 = 24 × 3 × 5 = 240

Let the required number be N

So, N = 240 × x + 7

Now use Hit and Trial method

When, x = 1

Then, N = 240 × 1 + 7 = 240 + 7 = 247

Hence, sum of the digits = 2 + 4 + 7 = 13

∴ 13 is the sum of the digits in the required smallest number which when divided by 48 and 60 leaves a remainder 7, but when divided by 13, the remainder is zero.

Share on Whatsapp

Stay updated with Quantitative Aptitude questions & answers with Testbook. Know more about Number System and ace the concept of LCM and HCF and LCM

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Trusted by 3,12,57,905+ Students

‹‹ Previous Ques Next Ques ››

## More LCM and HCF Questions

Q1. In a school there are 360, 520 and 280 students in classes 5, 6 and 7 respectively. Buses are to be hired to take these students for a trip. Find the maximum number of students who can be accommodated in each bus if each bus must take same number of students, and each bus should have students from the same class.Q2. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?Q3. Find the HCF of 245, 175 and 385.Q4. 5 bells tolls at an interval of 2, 4, 6, 8 and 12 minutes respectively. If all 5 bells tolls together at 10 am, then how many times they will toll together from 10 am to 12 noon?Q5. Suppose p and q are the LCM and HCF respectively of two positive numbers. If p : q = 14 : 1 and pq = 1134, then what is the difference between the two numbers?Q6. In the given below options which is the largest fraction?Q7. Three numbers are in the ratio 3 ∶ 5 ∶ 7 and their LCM is 840. Their HCF is:Q8. Consider the following statements: (A) A succession of numbers formed and arranged in a definite order according to certain definite rule, is called a progression. (B) Two numbers are said to be prime, if their H.C.F. is 2. (C) A number is divisible by 9, if the sum of its digits is divisible by 9. Choose the correct statements from above:Q9. Let x be the least number which when divided by 16, 24, 30, 36 and 45, the remainder in each case is 4, and x is divisible by 28. If the HCF of x and 3193 is y, then what is the sum of the digits of y?Q10. The sum of two numbers is 140. If their LCM is 240 and HCF is 20, then find the smaller number.

## More Number System Questions

Q1. If an 8-digit number 1862383A is divisible by 22, find the value of A.Q2. The least number by which 72 must be multiplied in order to produce a multiple of 112 isQ3. In a school there are 360, 520 and 280 students in classes 5, 6 and 7 respectively. Buses are to be hired to take these students for a trip. Find the maximum number of students who can be accommodated in each bus if each bus must take same number of students, and each bus should have students from the same class.Q4. Find the greatest value of k for which the 6-digit number 24312k is divisible by 6.Q5. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?Q6. If an 8-digit number 256139A4 is divisible by 11, find the value of A.Q7. If 23.5% of a number is 11.75, then what is the number?Q8. If x =

2+32−3

, then the value of (x - 7)2 is

Q9. Find the greatest value of (a + b) such than an 8-digit number 4523a60b is divisible by 15.Q10. If the square of a positive number is 6 more than five times the number, what is the number?

स्रोत : testbook.com

## What is the smallest natural number which when divided by 24, 18, 40 and 60 leave remainder 8 in each case?

Answer (1 of 6): LCM is the least no. /Smallest no. Which is divisible by all the given numbers. So, LCM of 24= 2× 2×2×3, 18= 2×3×3, 40= 2×2×2×5, 60=2×2×3×5, is all factors with greatest power, so LCM = 2^3 ×3^2 ×5^1= 8×9× 5 = 360. So , no. Leaves remainder 8 in each case is 360+8 = 368.

Division (mathematics)

Quantitative Aptitude

Math Competition Problems

Numbers (mathematics)

Mathematics

What is the smallest natural number which when divided by 24, 18, 40 and 60 leave remainder 8 in each case?

Ad by Amazon Web Services (AWS)

AWS is how.

AWS removes the complexity of building, training, and deploying machine learning models at any scale.

Ph.D. in Civil Engineering. Maths keeps one mentally active.Upvoted by

Krogi Us

, M.Sc. Mathematics & Computer Science, Aalto University (1988)Author has 52.3K answers and 32.9M answer viewsUpdated 4y

Factors of 24 = 2x2x2x3 18 = 2x3x3 40 = 2x2x2x5 60 = 2x2x3x5

LCM = 2x2x2x3x3x5 = 360

360+8 = 368. Answer is 368. Related questions

Which is the least number which when divided by 8, 12, and 16, leaves a remainder 7 in each case?

What is the smallest natural number which when divided by 24, 18, 40 and 60 leaves remainder 8 in each case?

What is the smallest natural number which is divided by 24, 18, and 40 leaving a number 8?

What is the lowest natural number which when divided by 14, 24, 2 and 10 leaves the remainder of 1 in each case?

What is the smallest number which, when divided by 24, 30 and 40, leaves no remainder?

Ali Dursen

M.S. in Mathematics, Sabanci University (Graduated 2013)Upvoted by

Michael Jørgensen

Such a number would be 8 greater than a number that is divisible by all those numbers. Since we want the smallest, answer is 0+8.

TARUN SHARMA

Works at MathematicsUpvoted by

Krogi Us

, M.Sc. Mathematics & Computer Science, Aalto University (1988)4y

LCM is the least no. /Smallest no. Which is divisible by all the given numbers. So, LCM of 24= 2× 2×2×3, 18= 2×3×3, 40= 2×2×2×5, 60=2×2×3×5, is all factors with greatest power, so LCM = 2^3 ×3^2 ×5^1= 8×9× 5 = 360. So , no. Leaves remainder 8 in each case is 360+8 = 368.

DigitalOcean

Simplifying cloud computingJul 6

Promoted

What is a step-by-step guide to learn cloud computing? I want to go from a beginner to advanced.

Helping people level up their cloud computing knowledge is what the DigitalOcean Community

Our general introduction to cloud computing

A Linux command line primer

How to use SQL

How to deploy a static website to the cloud with DigitalOcean App Platform

Ram Kushwah

B.Tech in Mathematics & Vipassanā (meditation), Malaviya National Institute of Technology, Jaipur (Graduated 1990)Author has 5K answers and 8.4M answer views2y

prime factors of 24,18,40 and 60 are:

24=2^3*3 18=2*3^2 40=2^3*5 60=2^2*3*5

Thus L;CM (24,18,40,60)=2^3 *3^2*5

=8*9*5=360

THE REMAINDER IN ALL CASES IS 8

HENCE THE NUMBER=LCM+8=368

Related questions

What is the smallest number that has a remainder of 7 if it is divided by 24 and 18?

What is the smallest four-digit number, when divided by 18 and 18 leaves a remainder of 8 in each case?

The cost of four mangoes, six guavas and sixteen watermelons is Rs. 500. The cost of seven mangoes, nine guavas and nineteen watermelon is Rs. 620. What is the cost of one mango, one guava and one watermelon, 120, 40, 150, or can't be determined?

What is the greatest number that will divide 18, 35, and 42 to leave the same remainder in each case?

What is the smallest number which when divided by 35 leaves remainder 30 ,when divided by 45 leaves remainder 40 and when divided by 55 leaves remainder 50?

Ellis Cave

40+ years as an Electrical EngineerAuthor has 5K answers and 2.6M answer views4y

Using the J programming language:

a#~*./8=18 24 40 60|/a=.1+i.1e3

8 368 728

There are three answers in the range 1–1000. The smallest is 8, as 8 divided by any larger number has a remainder of 8 (and a dividend of 0). So the answer is 8. The next-largest integer is 368 that meets all the criteria.

<<<<>>>>

“Civilization advances by extending the number of important operations which we can perform without thinking of them.”

B.Sc in Mathematics & Physics, Islamia College Gujranwala (Graduated 1977)Author has 24.1K answers and 12.8M answer views3y

24= 2 3 ×318=2× 3 2 40= 2 3 ×560= 2 2 ×3×5

24=23×318=2×3240=23×560=22×3×5

L.C.M. (24, 18, 40, 60) =

2 3 × 3 2 ×5=360

L.C.M. (24, 18, 40, 60) =23×32×5=360

⟹360 + 8 = 368 is the smallest number which when divided by

⟹360 + 8 = 368 is the smallest number which when divided by

24, 18, 40 and 60 leave remainder 8 in each case.

24, 18, 40 and 60 leave remainder 8 in each case.

Related questions

Which is the least number which when divided by 8, 12, and 16, leaves a remainder 7 in each case?

What is the smallest natural number which when divided by 24, 18, 40 and 60 leaves remainder 8 in each case?

What is the smallest natural number which is divided by 24, 18, and 40 leaving a number 8?

What is the lowest natural number which when divided by 14, 24, 2 and 10 leaves the remainder of 1 in each case?

स्रोत : www.quora.com