Question

find the largest number of 4 digits which is exactly divisible by 27 18 12 15​

Answer 1

Answer:

General Tip : If we are asked to find a number that is divisible by a set of numbers( a, b , c, d,... ), then that number is also divisible by their Least Common Multiplier (LCM).

In this case, the set of numbers is (12, 15, 18, 27). Their LCM will be divisible by all of these numbers from the set. Let’s find the LCM.

Steps to find the LCM:

The LCM is

12 = 3*4 = 2*2*3

(convert these numbers into prime factors)

15 = 3*5

18 = 2*3*3

27 = 3*3*3

LCM is found by multiplying the prime numbers with their maximum powers.

LCM = 3*3*3*2*2*5 (highest power of 3 is in 27, 2 in 12 and 5 in 15)

Hence LCM = 540

Now, the next part is easier.

The divisible numbers: 540*1, 540*2, .... , 540*n. (Where n is an integer.)

540*18 = 9720

540*19 = 10260 ( A FIVE DIGIT NUMBER)

Hence, the largest four-digit number divisible by 12, 15, 18, 27 is 9720.

Note: LCM itself is the smallest divisible number for a given set of numbers.

Step-by-step explanation:

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