Question

LCM lcm of 7,35,14,28​

Answer 1

Given: The numbers are$7,35,14,28$.

We have to find the LCM of the above number.

We are solving in the following way:

We have,

The numbers are$7,35,14,28$

Prime Factorization of $7$shows:

$7$is prime  =>  $7^1$

Prime Factorization of $14$is:

$2 \times 7 => 2^1 \times 7^1$

Prime Factorization of $28$is:

$2 \times 2 \times 7 => 2^2 \times 7^1$

Prime Factorization of $35$ is:

$5 \times 7 => 5^1 \times 7^1$

For each prime factor, we will find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

$2, 2, 5, 7$

Multiplying these factors together to find the LCM.

LCM $= 2 \times 2 \times 5 \times 7 = 140$

In exponential form:

LCM = $2^2 \times 5^1 \times 7^1 = 140$

LCM = $140$

Hence, the LCM of the above number is$140$.

Answer 2

In context to question asked,

We have to determine the HCF of given number.

As per question,

We have, numbers - 7, 35, 14, 28

As we know that,

LCM of two or more number are that particular number which is lowest number which is also a common multiple of all the given number.

So, for determining the LCM of given number we will use prime factorization method.

Hence, Prime factorization of given number will be,

$7 = 7\times 1\\14 = 7\times 2\\28 = 7\times 2 \times 2\\35 = 7\times 5\\=>LCM = 7\times 2\times 2\times 5=140$

Hence, LCM of the given number will be 140