Given Numbers are 42, 46

We can find the LCM of 42, 46 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 42 and 46

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

Multiples of 46 =46,92,138,184,230,276,322,368,414,460,506,552,598,644,690,736,782,

Now, get the least common multiple of 42, 46 which is 966

So, the LCM of 42, 46 is 966.

One method for determining the LCM of 42 and 46 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 42's prime factorization:

Prime factors of 42 are 2, 3,7.

42 = 2¹×3¹×7¹

And this is 46's prime factorization:

Prime factors of 46 are 2,23.

46 = 2¹×23¹

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: 2, 3,7,23

2¹×3¹×7¹×23¹ = 966

This shows that the LCM of 42 and 46 is 966.

The first step in determining the Least Common Multiple of 42 and 46 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 42 and 46:

Lets look at the first ten multiples of these numbers, 42 and 46:

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

46,92,138,184,230,276,322,368,414,782 are the first ten multiples of 46.

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 42 and 46, for example, are 504, 714, and 736. 966 is the least common multiple since it is the smallest.

42 and 46 have an LCM of 966.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42 and 46, than apply into the LCM equation.

GCF(42,46) = 2
LCM(42,46) = ( 42 × 46) / 2
LCM(42,46) = 1932 / 2
LCM(42,46) = 966

1. What is the LCM of 42 and 46?

The LCM of 42 and 46 is 966.

2. How to find the lowest common multiple of 42 and 46?

To find the lowest common multiple of 42 and 46, we have to get the multip;es of both numbers and identify the least common multiple in them which is 966.

3. 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.

4. What are the Factors of 46?

Answer: Factors of 46 are 1, 2, 23, 46. There are 4 integers that are factors of 46. The greatest factor of 46 is 46.

Answer:

Least Common Multiple of 42 and 46 = 966

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 46

46 = 2 x 23

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

LCM = 966 = 2 x 3 x 7 x 23

Step 4: Therefore, the least common multiple of 42 and 46 is 966.