if you want to remove an article from website contact us from top.

    the lcm of least composite number and least perfect square number is

    Mohammed

    Guys, does anyone know the answer?

    get the lcm of least composite number and least perfect square number is from screen.

    Find the LCM of smallest composite number and smallest prime number. [Solved]

    The LCM of smallest composite number and smallest prime number is 4

    Find the LCM of the smallest composite number and the smallest prime number.

    Prime numbers are the numbers that have only two factors, that are, 1 and the number itself.

    Answer: The LCM of the smallest composite number and the smallest prime number is 4.

    Composite numbers can be defined as natural numbers that have more than two factors.

    Explanation:

    The smallest prime number is 2.

    The smallest composite number is 4.

    To find the LCM of 2 and 4 let's do their prime factorization.

    2 = 2 4 = 2 × 2

    LCM(2, 4) = 2 × 2 = 4

    Thus, the LCM of the smallest composite number and the smallest prime number is 4.

    स्रोत : www.cuemath.com

    [Solved] What is the least perfect square that is a multiple of 7, 11

    Given: The numbers = 7, 11, 12 Concept: LCM = The LCM of the numbers is the smallest number that is the multiple of every one of the numbers Calculation: L

    Home Mathematics Number System

    Question

    Download Solution PDF

    What is the least perfect square that is a multiple of 7, 11 and 12?

    This question was previously asked in

    DSSSB AE Civil 26 Sept 2021 Official Paper

    Download PDF Attempt Online

    View all DSSSB AE Papers >

    45000 853776 213444 8100

    Answer (Detailed Solution Below)

    Option 3 : 213444

    Crack AE & JE - Civil with

    India's Super Teachers

    FREE

    Demo Classes Available*

    Explore Supercoaching For FREE

    Free Tests

    View all Free tests >

    FREE

    Environmental Engineering Free Mock

    2K Users

    20 Questions 20 Marks 14 Mins

    Start Now

    Detailed Solution

    Download Solution PDF

    Given:

    The numbers = 7, 11, 12

    Concept:

    LCM = The LCM of the numbers is the smallest number that is the multiple of every one of the numbers

    Calculation:

    Let us assume the least perfect square be X

    ⇒ 7 = 7 × 1 ⇒ 11 = 11 × 1 ⇒ 12 = 22 × 3

    ⇒ The LCM of (7, 11, 12) = 22 × 3 × 11 × 7

    ⇒ The least perfect square = 22 × 32 × 112 × 72 = 213444

    ∴ The required result will be 213444.

    Download Solution PDF

    Share on Whatsapp

    Win over the concepts of Number System and get a step ahead with the preparations for Mathematics with Testbook.

    India’s #1 Learning Platform

    Start Complete Exam Preparation

    Daily Live MasterClasses

    Practice Question Bank

    Mock Tests & Quizzes

    Get Started for Free

    Download App

    Trusted by 3,19,01,930+ Students

    ‹‹ Previous Ques Next Ques ››

    More Number System Questions

    Q1. Given below are two statements Statement I: A number that has factors other than 1 and itself is called a composite number Statement II: 23 is the only odd prime number In light of the above statements, choose the correct answer from the options given belowQ2. The unit digit of the product of first 22 natural number isQ3. If set A = {1, 2, 3, 4, 5,…} is given, then it represents:Q4. What is the result when 0.27272727... is converted to a fraction?Q5. What will be the eventual bank balance when a deposit of Rs.900.25 and a withdrawal of Rs.650.57 is made to an account balance of Rs.1350.14?Q6. A man has Rs.85 in coins of 2-rupee, 5 - rupees and 10 - rupees. The number of coins of each denomination is equal. What is the total number of coins he has?Q7. What will be the result when 0.36363636... is converted to a fraction?Q8. Find the greatest number which divides 36, 64 and 92 in such a way that in each case same remainder is left.Q9. What is the least perfect square that is a multiple of 7, 11 and 12?Q10. What must be added to 45680 to make it exactly divisible by 9?

    स्रोत : testbook.com

    The least perfect square number which is divisible class 7 maths CBSE

    The least perfect square number which is divisible by 8 15 20 22 is A 435600 B 43560 C 39600 D None

    The least perfect square number which is divisible by 8, 15, 20, 22 is

    A. 435600 B. 43560 C. 39600 D. None Answer Verified 204.6k+ views

    Hint: LCM (Least Common Multiple) of a set of numbers is the least number which is a multiple of all of them, or which is divisible by all the numbers of the set.

    Any multiple of LCM will also be divisible by the numbers of the set, but it would no longer be the least.

    A perfect square can be written as a product of two identical numbers.

    Complete step-by-step answer:

    Let us first find the LCM of the given numbers by factoring them into prime numbers:

    8= 2 3 8=23 15=3×5 15=3×5 22=2×11 22=2×11 20= 2 2 ×5 20=22×5

    Since an LCM is a multiple of all of them, it must have at least the maximum power of all the prime numbers present in it.

    ∴ The LCM will be 2 3 ×3×5×11 23×3×5×11 .

    Now we want a number which should be divisible by all the given numbers, so it must be a multiple of the LCM.

    Since, the number we want must also be a perfect square, we need to find a multiple of the LCM which can be written as a product of two identical numbers.

    But a prime number cannot be divided into parts, so we must multiply the LCM with a number so that every power of the prime numbers in the group becomes an even power (can be separated into two identical parts).

    The least such perfect square will be obtained if we multiply the LCM by 2 × 3 × 5 × 11 to give

    2 4 × 3 2 × 5 2 × 11 2 24×32×52×112 .

    We can calculate its value as well: 16 × 9 × 25 × 121 = 453600.

    ∴ The answer is A. 453600.

    Note: There are infinitely many perfect square common multiples, but the least one is obtained by multiplying the LCM with the least such number that gives even powers for all its prime factors.

    Similarly, we can find least cube common factors or other higher-powered common factors.

    Prime Numbers: The numbers which have exactly two factors, i.e. they are not divisible by any other number except for 1 and themselves, are called prime numbers. All other numbers are called composite numbers. 1 is neither prime (it has exactly one factor!), nor composite.

    स्रोत : www.vedantu.com

    Do you want to see answer or more ?
    Mohammed 4 month ago
    4

    Guys, does anyone know the answer?

    Click For Answer