Given Numbers are 76, 84

We can find the LCM of 76, 84 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 76 and 84

Multiples of 76 =76,152,228,304,380,456,532,608,684,760,836,912,988,1064,1140,1216,1292,

Multiples of 84 =84,168,252,336,420,504,588,672,756,840,924,1008,1092,1176,1260,1344,1428,

Now, get the least common multiple of 76, 84 which is 1596

So, the LCM of 76, 84 is 1596.

One method for determining the LCM of 76 and 84 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 76's prime factorization:

Prime factors of 76 are 2,19.

76 = 2²×19¹

And this is 84's prime factorization:

Prime factors of 84 are 2, 3,7.

84 = 2²×3¹×7¹

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: 2,19, 3,7

2²×3¹×7¹×19¹ = 1596

This shows that the LCM of 76 and 84 is 1596.

The first step in determining the Least Common Multiple of 76 and 84 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 76 and 84:

Lets look at the first ten multiples of these numbers, 76 and 84:

76,152,228,304,380,456,532,608,684,1292 are the first ten multiples of 76.

84,168,252,336,420,504,588,672,756,1428 are the first ten multiples of 84.

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 76 and 84, for example, are 912, 1292, and 1344. 1596 is the least common multiple since it is the smallest.

76 and 84 have an LCM of 1596.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76 and 84, than apply into the LCM equation.

GCF(76,84) = 4
LCM(76,84) = ( 76 × 84) / 4
LCM(76,84) = 6384 / 4
LCM(76,84) = 1596

1. What is the LCM of 76 and 84?

The LCM of 76 and 84 is 1596.

2. How to find the lowest common multiple of 76 and 84?

To find the lowest common multiple of 76 and 84, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1596.

3. What are the Factors of 76?

Answer: Factors of 76 are 1, 2, 4, 19, 38, 76. There are 6 integers that are factors of 76. The greatest factor of 76 is 76.

4. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

Answer:

Least Common Multiple of 76 and 84 = 1596

Step 1: Find the prime factorization of 76

76 = 2 x 2 x 19

Step 2: Find the prime factorization of 84

84 = 2 x 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 = 1596 = 2 x 2 x 3 x 7 x 19

Step 4: Therefore, the least common multiple of 76 and 84 is 1596.