Given Numbers are 7035, 7042

We can find the LCM of 7035, 7042 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 7035 and 7042

Multiples of 7035 =7035,14070,21105,28140,35175,42210,49245,56280,63315,70350,77385,84420,91455,98490,105525,112560,119595,

Multiples of 7042 =7042,14084,21126,28168,35210,42252,49294,56336,63378,70420,77462,84504,91546,98588,105630,112672,119714,

Now, get the least common multiple of 7035, 7042 which is 7077210

So, the LCM of 7035, 7042 is 7077210.

One method for determining the LCM of 7035 and 7042 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:

Here is 7035's prime factorization:

Prime factors of 7035 are 3, 5, 7,67.

7035 = 3¹×5¹×7¹×67¹

And this is 7042's prime factorization:

Prime factors of 7042 are 2, 7,503.

7042 = 2¹×7¹×503¹

When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 3, 5, 7,67, 2,503

2¹×3¹×5¹×7¹×67¹×503¹ = 7077210

This shows that the LCM of 7035 and 7042 is 7077210.

The first step in determining the Least Common Multiple of 7035 and 7042 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 7035 and 7042:

Lets look at the first ten multiples of these numbers, 7035 and 7042:

7035,14070,21105,28140,35175,42210,49245,56280,63315,119595 are the first ten multiples of 7035.

7042,14084,21126,28168,35210,42252,49294,56336,63378,119714 are the first ten multiples of 7042.

You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 7035 and 7042, for example, are 84420, 119595, and 112672. 7077210 is the least common multiple since it is the smallest.

7035 and 7042 have an LCM of 7077210.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7035 and 7042, than apply into the LCM equation.

GCF(7035,7042) = 7
LCM(7035,7042) = ( 7035 × 7042) / 7
LCM(7035,7042) = 49540470 / 7
LCM(7035,7042) = 7077210

1. What is the LCM of 7035 and 7042?

The LCM of 7035 and 7042 is 7077210.

2. How to find the lowest common multiple of 7035 and 7042?

To find the lowest common multiple of 7035 and 7042, we have to get the multip;es of both numbers and identify the least common multiple in them which is 7077210.

3. What are the Factors of 7035?

Answer: Factors of 7035 are 1, 3, 5, 7, 15, 21, 35, 67, 105, 201, 335, 469, 1005, 1407, 2345, 7035. There are 16 integers that are factors of 7035. The greatest factor of 7035 is 7035.

4. What are the Factors of 7042?

Answer: Factors of 7042 are 1, 2, 7, 14, 503, 1006, 3521, 7042. There are 8 integers that are factors of 7042. The greatest factor of 7042 is 7042.

Answer:

Least Common Multiple of 7035 and 7042 = 7077210

Step 1: Find the prime factorization of 7035

7035 = 3 x 5 x 7 x 67

Step 2: Find the prime factorization of 7042

7042 = 2 x 7 x 503

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 7077210 = 2 x 3 x 5 x 7 x 67 x 503

Step 4: Therefore, the least common multiple of 7035 and 7042 is 7077210.