Question

least no.t
hat is exactly divisible by 24, 28,36,48​

Answer 1

Step-by-step explanation:

First, we need to find the LCM of 24, 36 and 48. The LCM of 24, 36 and 48 is 144.

Now, we shall find the difference of 24 and 21 which is 3. Similarly, the difference of 36 and 33 and also that of 48 and 45 is 3 respectively.

The difference between the LCM and 3 is the smallest number.

So, 144 - 3 = 141.

Hence, 141 is the smallest number when divided by 24, 36 and 48 leave remainders 21, 33 and 45 respectively.

Answer 2

Given :  Number exactly divisible by 24, 28,36,48​

To Find : Least Number

Solution:

To find least number exactly divisible by 24, 28,36,48​

Need to find LCM ( 24 , 28 , 36 , 48)

LCM  - Least common multiplier of given numbers is the least number which is perfectly divisible by given numbers.

LCM = product of each factor  of highest power

24 = 2 * 2 * 2 * 3  = 2³ * 3¹

28 = 2 * 2 * 7  = 2² * 7¹

36 = 2 * 2 * 3 * 3 = 2² * 3²

48 = 2 * 2 * 2 * 2 * 3 = 2⁴ * 3¹

LCM = 2⁴ * 3² * 7¹

= 16 * 9 * 7

=  144 * 7

= 1008

1008 is the  least number exactly divisible by 24, 28,36,48​

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