Find the greatest number of 4 digit which is exactly divisible by 15 24 and 36

Prime factorization: 15 = 3 × 5 24 = 2 3 × 3 36 = 2 2 × 3 2 LCM = product of greatest power of each prime factor involved in the numbers = 2 3 × 3 2 × 5 = 360 Now, the greatest four digit number is 9999. On dividing 9999 by 360 we get 279 as remainder. Thus, 9999 – 279 = 9720 is exactly divisible by 360. Hence, the greatest number of four digits which is exactly divisible by 15, 24 and 36 is 9720.

Prime factorization: 15 = 3 × 5 24 = 2 3× 3 36 = 2 2× 3 2 LCM = product of greatest power of each prime factor involved in the numbers = 2 3× 3 2× 5 = 360 Now, the greatest four digit number is 9999. On dividing 9999 by 360 we get 279 as remainder. Thus, 9999 – 279 = 9720 is exactly divisible by 360. Hence, the greatest number of four digits which is exactly divisible by 15, 24 and 36 is 9720.

Hint: - LCM is elaborated as Least Common Multiple, which is the lowest common factor among the integers. To find the LCM of the given numbers (Lowest common number), which is divisible by all numbers, the method includes basic factorization of the numbers to find factors that are multiplied together to form a number. Complete step-by-step answer: In this question, to find the largest number which will be exactly divisible by the given numbers, find their LCM by finding the factors and divide the LCM with the largest number 9999 to check whether they are divisible and if not find the difference. Given the numbers are 12, 15, 18 and 27 The largest 4 digit number known is 9999 For largest number find the LCM by factorizing of the numbers \[ 2\underline \right) = 9720\] The number is exactly divisible by 540 hence 9720 is the largest 4 digit number divisible by 12, 15, 18 and 27. Note: LCM of given numbers is exactly divisible by each of the numbers. During the LCM calculation, students must know the tables of various numbers, and they have to perform the operations step by step. Lastly, they have to multiply all the numbers by which they are dividing the given set of numbers.

8 = 1 × 2 × 2 × 2 = 2 3 12 = 1 × 2 × 2 × 3 = 2 2 × 3 1 18 = 1 × 2 × 3 × 3 = 2 1 × 3 2 30 = 1 × 2 × 3 × 5 = 2 1× 3 1 × 5 1 LCM of 8, 12, 18, and 30 = 2 3× 3 2× 5 1 = 360 Largest 4-digit number is 9999 Now, if we divide 9999 by 360, we will get 27.78 as quotient. The integer just less than 27.78 is 27 ∴ Required number = 360 × 27 = 9720 Hence, the greatest number of four digits which is exactly divisible by each of 8, 12, 18 and 30 is 9720.

Views: 6,043 5.1 1. In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (i) The taxi fare after each km when the fare is ₹15 for the first km and ₹8 for each additional km. (ii) The amount of air present in a cylinder when a vacuum pump removes 4 1 ​ of the air remaining in the cylinder at a time. (iii) The cost of digging a well after every metre of digging, when it costs ₹150 for the first metre and rises by ₹ 50 for each subsequent metre. (iv) The amount of money in the account every year, when ₹ 10000 is deposited at compound interest at 8% per annum. 2. Write first four terms of the AP, when the first term a and the common difference d are given as follows: (i) a = 10 , d = 10 (ii) a = − 2 , d = 0 (iii) a = 4 , d = − 3 (iv) a = − 1 , d = 2 1 ​ (v) a = − 1.25 , d = − 0.25 3. For the following APs, write the first term and the common difference: (i) 3 , 1 , − 1 , − 3 , … (ii) − 5 , − 1 , 3 , 7 , … (iii) 3 1 ​ , 3 5 ​ , 3 9 ​ , 3 13 ​ , … (iv) 0.6 , 1.7 , 2.8 , 3.9 , … 4. Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. (i) 2 , 4 , 8 , 16 , … (ii) 2 , 2 5 ​ , 3 , 2 7 ​ , … (iii) − 1.2 , − 3.2 , − 5.2 , − 7.2 , … (iv) − 10 , − 6 , − 2 , 2 , … (v) 3 , 3 + 2 ​ , 3 + 2 2 ​ , 3 + 3 2 ​ , … (vi) 0.2 , 0.22 , 0.222 , 0.2222 , … (vii) 0 , − 4 , − 8 , − 12 , … (viii) − 2 1 ​ , − 2 1 ​ , − 2 1 ​ , − 2 1 ​ , … 20. Find the greatest number of four digits which is...

SOLUTION Hey, The answer is :9720 Here is a step - by - step procedure to find the greatest four digit number that is exactly divisible by15,24,36. • Find the LCM (Least common multiple) of 15, 24, 36. Any number divisible by the LCM of the 15,24,36 will be divisible by each of15,24,36. • To find LCM, write each number as a product of its prime factors. • 15=3∗5=3∗5———————————————15 has one 3 and one 5. • 24=2∗2∗2∗3———————————24 has three 2’s and one 3. • 36=2∗2∗3∗3———————————36 has two 2’s and two 3’s. • To get the LCM: Multiply each factor the greatest number of times it occurs in any of the numbers. • There are 3 factors :2,3,5 • The greatest number of times 2 occurs in the numbers (15, 24, 36) : Three • The greatest number of times 3 occurs in the numbers (15, 24, 36) : Two • The greatest number of times 5 occurs in the numbers (15, 24, 36) : One • LCM =2∗2∗2∗3∗3∗5=360 2. To Find the greatest four digit number divisible by 360: • The greatest four digit number is9999 • 9999 when divided by 360 is 27.75 ( 27.75 is not an integer, thus 9999 is not divisible by 360. ) • The greatest four digit number divided by 360 would be =360∗27=9720 ( Note : 27 is the part of the number before the decimal point in 27.75) 3. We can check if 9720 is divisible by each of 15, 24, 36 • 9720/15=648 • 9720/24=405 • 9720/36=270