Practice: Finding common multiples

The least common multiple is 72. hence 1000 divided by 72 comes to 13.

8's prime factorization is 2,2,2. 36's prime factorization is 2,2,3,3. 24's prime factorization is 2,2,2,3.

A common multiple of all three of these numbers will be divisible by their least common multiple. That is, each of our numbers will need to have a prime factorization that consists of at least 3 2's (as 24 has 3 2's) and 2 3's (as 36 has 2 3's).

In other words, each of our numbers will need to be divisible by 2(2)(2)(3)(3) = 72.

Take the floor of 1000/72 and you get 13!

The least common multiple of 8, 24 and 36 is 72 .

$8 = 2^{3}$

$24 = 2^{3} \times 3$

$36 = 2^{2} \times 3^{2}$

$LCM = 2^{3} \times 3^{2} = 72$

Hence the common multiples of 8,24, and 36 are multiples of 72. Dividing 1000 by 72, we get 13 with the remainder 64.

13 is the answer.

1000/lcm(8,36,24)

LCM of 8,36 and 24 =72 solve using the formula an=a+(n-1)d where a=72, d=72 and an=936. solving we get n=13 which is the required number

The LCM of $8, 36, 24$ is 72. Therefore, our answer is the floor of $\frac{1000}{72} = \boxed{13}$

LCM of 8,24,36= 72 thus, all multiples of 72 less than 1000 would also be the multiples of 8, 24 and 36 Hence, first 13 multiples of 72 would be the answer.

By Calculating least common multiplier is 72 , and 1000/72 is 13.

1000 / 72 = 13,88....

x = 13

common multiple of 8,36,and 24 is 72. 72 has 13 multiple up to 1000

The numbers are multiples of 72 which is LCM of 8, 36, 24

1000 ÷ 72 quotient is 13 numbers are multiple of three numbers 8,36, and 24.

Lowest Common Multiple of 8,36 and 24 is 72. we know that all the multiple of 72 would also be multiple of 8, 36 and 24

thus 1000/72=13(only positive integers)

First integer is 72. 1000/72=13.88. As less than or equal to 1000, the answer is 13.

take LCM of all Digits and Divide 1000/LCM

take LCM of 8,36,24. LCM= 72 divide 1000 by 72 neglect the decimal portion.

first calculate the GCD of (8,36,24) GCD calculation : 8-2^3 ;36-2^2 3^2; 24-2^3 3 and take the highest prime powers in each integer that is 2^3*3^2=72 then find 1000/72 neglect the remainder then the result is 13