Question

In a class there are less than 500 students . when it is divided by 3 it gives a whole number. similarly when it is divided by 4,5 or 7 gives a whole number. find the no. of students in the class ans: 420

Answer 1

no: of students is less than 500
When no: of students is divided by 3,4,5,7 we get a whole number, that is, remainder =0
Hence, find the L.C.M of 3,4,5,7
L.C.M = 3*4*5*7 =  420
Hence number of students = 420.

Answer 2

There are 420 students in the class.

Explanation: In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD). As an illustration, LCM (4, 5) = 20. In this case, the LCM 20 may be divided by both 4 and 5, hence these two numbers are referred to as the divisors of 20.

When the fractions' denominators differ, LCM can also be used to add or subtract any two fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction. The simplifying process is facilitated by this procedure.

Given, that the no. of students in a class is less than 500.

Let it be n

When n is divided by 3, 4, 5, and 7; it gives a whole no. in each case.

So, n is a multiple of LCM (Least Common Factor) of 3, 4, 5, 7

As 3, 5 and 7 are prime nos, and 4 is not divisible by any of them,

$\therefore$ LCM= $3\times 4\times 5\times 7=420$

n is a multiple of 420

$\therefore$ n=420k

But given, $n < 500$

$\therefore n=420$

There are 420 students in the class.

To learn more about LCM, click on the links below:

https://brainly.in/question/730856?msp_srt_exp=5

https://brainly.in/question/14102195?msp_srt_exp=5

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