Question

find the greatest 3 digit number exactly divisible by 6 10 and 12​

Answer 1

Step-by-step explanation:

LCM of 6,8 and 12 is 24.

now we have to find multiple of 24 which is the smallest 3 digit number.

answer=24 x 5=120

Answer for 2nd part

LCM of 8,10 and 12 is 120

. now we have to find multiple of 120 which is the greatest 3 digit number.

Answer=120 x 8=960

Answer 2

Given: Three numbers 6, 10 and 12

To find: The greatest 3 digit number exactly divisible by the given numbers

Solution: The required number is the greatest 3 digit multiple of Least Common Multiple of 6, 10 and 12

Using Prime factorization method:

6 = 2 × 3

10 = 2 × 5

12 = 2 × 2 × 3

LCM is the product of maximum frequencies of all the factors of given numbers.

LCM = 2 × 2 × 3 × 5 = 60

The required number is the greatest 3 digit multiple of 60.

Now, 60 × 16 = 960

Hence, the greatest 3 digit number exactly divisible by 6, 10 and 12 is 960.