Question

Find the smallest number of five digits exactly divisible by 16, 24, 36 and 54 formula

Answer 1

Answer:

Step-by-step explanation:

First find the LCM of 16,24,36 and 54.

LCM=432.

Smallest 5 - digit no.=10000

Divide 10000 by 432.

Remainder=64

Req. no. = 10000+(432-64)

             =10000+368

             =10368

Ans.10368 is the smallest 5 digit no. exactly divisible by 16,24,36 and 54

Answer 2

Given: Four numbers- 16, 24, 36 and 54

To find: The smallest five digit number exactly divisible by the given numbers

Solution:

To find the required number, first we need to find the smallest number which is exactly divisible by the given numbers i.e., their LCM.

Using prime factorization:

16 = 2 × 2 × 2 × 2

24 = 2 × 2 × 2 × 3

36 = 2 × 2 × 3 × 3

54 = 2 × 3 × 3 × 3

LCM is the product of maximum frequencies of numbers occuring as the factors of given numbers.

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432

432 is the smallest number which is exactly divisible by the given numbers.

The required number is the least five digit multiple of 432.

We get, 432 × 24 = 10368

Hence, 10368 is the smallest five digit number exactly divisible by 16, 24, 36 and 54.