Least Common Multiple of 75678 and 75686

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 75678 and 75686 by Prime method
• Least Common Multiple of 75678 and 75686 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 75678 and 75686. First we will calculate the prime factors of 75678 and 75686.

Prime Factorization of 75678

Prime factors of 75678 are 2, 3,12613. Prime factorization of 75678 in exponential form is:

75678 = 2¹×3¹×12613¹

Prime Factorization of 75686

Prime factors of 75686 are 2, 13, 41,71. Prime factorization of 75686 in exponential form is:

75686 = 2¹×13¹×41¹×71¹

Now multiplying the highest exponent prime factors to calculate the LCM of 75678 and 75686.

LCM(75678,75686) = 2¹×3¹×13¹×41¹×71¹×12613¹
LCM(75678,75686) = 2863882554

Factors of 75678

List of positive integer factors of 75678 that divides 75678 without a remainder.

1, 2, 3, 6, 12613, 25226, 37839, 75678

Factors of 75686

List of positive integer factors of 75686 that divides 75686 without a remainder.

1, 2, 13, 26, 41, 71, 82, 142, 533, 923, 1066, 1846, 2911, 5822, 37843, 75686

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75678 and 75686, than apply into the LCM equation.

GCF(75678,75686) = 2
LCM(75678,75686) = ( 75678 × 75686) / 2
LCM(75678,75686) = 5727765108 / 2
LCM(75678,75686) = 2863882554

(i) The LCM of 75686 and 75678 is associative

LCM of 75678 and 75686 = LCM of 75686 and 75678

1. What is the LCM of 75678 and 75686?

Answer: LCM of 75678 and 75686 is 2863882554.

2. What are the Factors of 75678?

Answer: Factors of 75678 are 1, 2, 3, 6, 12613, 25226, 37839, 75678. There are 8 integers that are factors of 75678. The greatest factor of 75678 is 75678.

3. What are the Factors of 75686?

Answer: Factors of 75686 are 1, 2, 13, 26, 41, 71, 82, 142, 533, 923, 1066, 1846, 2911, 5822, 37843, 75686. There are 16 integers that are factors of 75686. The greatest factor of 75686 is 75686.

4. How to Find the LCM of 75678 and 75686?

Answer:

Least Common Multiple of 75678 and 75686 = 2863882554

Step 1: Find the prime factorization of 75678

75678 = 2 x 3 x 12613

Step 2: Find the prime factorization of 75686

75686 = 2 x 13 x 41 x 71

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

LCM = 2863882554 = 2 x 3 x 13 x 41 x 71 x 12613

Step 4: Therefore, the least common multiple of 75678 and 75686 is 2863882554.