Least Common Multiple of 75693 and 75700

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

• Least Common Multiple of 75693 and 75700 by Prime method
• Least Common Multiple of 75693 and 75700 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 75693 and 75700. First we will calculate the prime factors of 75693 and 75700.

Prime Factorization of 75693

Prime factors of 75693 are 3, 23,1097. Prime factorization of 75693 in exponential form is:

75693 = 3¹×23¹×1097¹

Prime Factorization of 75700

Prime factors of 75700 are 2, 5,757. Prime factorization of 75700 in exponential form is:

75700 = 2²×5²×757¹

Now multiplying the highest exponent prime factors to calculate the LCM of 75693 and 75700.

LCM(75693,75700) = 2²×3¹×5²×23¹×757¹×1097¹
LCM(75693,75700) = 5729960100

Factors of 75693

List of positive integer factors of 75693 that divides 75693 without a remainder.

1, 3, 23, 69, 1097, 3291, 25231, 75693

Factors of 75700

List of positive integer factors of 75700 that divides 75700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 757, 1514, 3028, 3785, 7570, 15140, 18925, 37850, 75700

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75693 and 75700, than apply into the LCM equation.

GCF(75693,75700) = 1
LCM(75693,75700) = ( 75693 × 75700) / 1
LCM(75693,75700) = 5729960100 / 1
LCM(75693,75700) = 5729960100

(i) The LCM of 75700 and 75693 is associative

LCM of 75693 and 75700 = LCM of 75700 and 75693

1. What is the LCM of 75693 and 75700?

Answer: LCM of 75693 and 75700 is 5729960100.

2. What are the Factors of 75693?

Answer: Factors of 75693 are 1, 3, 23, 69, 1097, 3291, 25231, 75693. There are 8 integers that are factors of 75693. The greatest factor of 75693 is 75693.

3. What are the Factors of 75700?

Answer: Factors of 75700 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 757, 1514, 3028, 3785, 7570, 15140, 18925, 37850, 75700. There are 18 integers that are factors of 75700. The greatest factor of 75700 is 75700.

4. How to Find the LCM of 75693 and 75700?

Answer:

Least Common Multiple of 75693 and 75700 = 5729960100

Step 1: Find the prime factorization of 75693

75693 = 3 x 23 x 1097

Step 2: Find the prime factorization of 75700

75700 = 2 x 2 x 5 x 5 x 757

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

LCM = 5729960100 = 2 x 2 x 3 x 5 x 5 x 23 x 757 x 1097

Step 4: Therefore, the least common multiple of 75693 and 75700 is 5729960100.