Given Numbers are 35, 42

We can find the LCM of 35, 42 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 35 and 42

Multiples of 35 =35,70,105,140,175,210,245,280,315,350,385,420,455,490,525,560,595,

Multiples of 42 =42,84,126,168,210,252,294,336,378,420,462,504,546,588,630,672,714,

Now, get the least common multiple of 35, 42 which is 210

So, the LCM of 35, 42 is 210.

One method for determining the LCM of 35 and 42 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 35's prime factorization:

Prime factors of 35 are 5,7.

35 = 5¹×7¹

And this is 42's prime factorization:

Prime factors of 42 are 2, 3,7.

42 = 2¹×3¹×7¹

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: 5,7, 2,3

2¹×3¹×5¹×7¹ = 210

This shows that the LCM of 35 and 42 is 210.

The first step in determining the Least Common Multiple of 35 and 42 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 35 and 42:

Lets look at the first ten multiples of these numbers, 35 and 42:

35,70,105,140,175,210,245,280,315,595 are the first ten multiples of 35.

42,84,126,168,210,252,294,336,378,714 are the first ten multiples of 42.

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 35 and 42, for example, are 420, 595, and 672. 210 is the least common multiple since it is the smallest.

35 and 42 have an LCM of 210.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 35 and 42, than apply into the LCM equation.

GCF(35,42) = 7
LCM(35,42) = ( 35 × 42) / 7
LCM(35,42) = 1470 / 7
LCM(35,42) = 210

1. What is the LCM of 35 and 42?

The LCM of 35 and 42 is 210.

2. How to find the lowest common multiple of 35 and 42?

To find the lowest common multiple of 35 and 42, we have to get the multip;es of both numbers and identify the least common multiple in them which is 210.

3. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

4. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

Answer:

Least Common Multiple of 35 and 42 = 210

Step 1: Find the prime factorization of 35

35 = 5 x 7

Step 2: Find the prime factorization of 42

42 = 2 x 3 x 7

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

LCM = 210 = 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 35 and 42 is 210.