Least Common Multiple of 6069 and 6075

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6069 and 6075 the smallest integer that is 12289725 that is divisible by both numbers.

Least Common Multiple (LCM) of 6069 and 6075 is 12289725.

LCM(6069,6075) = 12289725

LCM of 6069 and 6075

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

LCM of:
and

Least Common Multiple of 6069 and 6075

LCM of 6069 and 6075 is 12289725

Least common multiple can be found by multiplying the highest exponent prime factors of 6069 and 6075. First we will calculate the prime factors of 6069 and 6075.

Prime Factorization of 6069


3 6069
7 2023
17 289
17 17
1

Prime factors of 6069 are 3, 7,17. Prime factorization of 6069 in exponential form is:

6069 = 31×71×172

Prime Factorization of 6075


3 6075
3 2025
3 675
3 225
3 75
5 25
5 5
1

Prime factors of 6075 are 3,5. Prime factorization of 6075 in exponential form is:

6075 = 35×52

Now multiplying the highest exponent prime factors to calculate the LCM of 6069 and 6075.

LCM(6069,6075) = 35×52×71×172
LCM(6069,6075) = 12289725

Factors of 6069

List of positive integer factors of 6069 that divides 6069 without a remainder.

1, 3, 7, 17, 21, 51, 119, 289, 357, 867, 2023, 6069

Factors of 6075

List of positive integer factors of 6075 that divides 6075 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 243, 405, 675, 1215, 2025, 6075

Least Common Multiple of 6069 and 6075 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6069 and 6075, than apply into the LCM equation.

GCF(6069,6075) = 3
LCM(6069,6075) = ( 6069 × 6075) / 3
LCM(6069,6075) = 36869175 / 3
LCM(6069,6075) = 12289725

Properties of LCM 6069 and 6075

(i) The LCM of 6075 and 6069 is associative

LCM of 6069 and 6075 = LCM of 6075 and 6069

Related Least Common Multiples of 6069

Related Least Common Multiples of 6075

Frequently Asked Questions on LCM of 6069 and 6075

1. What is the LCM of 6069 and 6075?

Answer: LCM of 6069 and 6075 is 12289725.

2. What are the Factors of 6069?

Answer: Factors of 6069 are 1, 3, 7, 17, 21, 51, 119, 289, 357, 867, 2023, 6069. There are 12 integers that are factors of 6069. The greatest factor of 6069 is 6069.

3. What are the Factors of 6075?

Answer: Factors of 6075 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 243, 405, 675, 1215, 2025, 6075. There are 18 integers that are factors of 6075. The greatest factor of 6075 is 6075.

4. How to Find the LCM of 6069 and 6075?

Answer:

Least Common Multiple of 6069 and 6075 = 12289725

Step 1: Find the prime factorization of 6069

6069 = 3 x 7 x 17 x 17

Step 2: Find the prime factorization of 6075

6075 = 3 x 3 x 3 x 3 x 3 x 5 x 5

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

LCM = 12289725 = 3 x 3 x 3 x 3 x 3 x 5 x 5 x 7 x 17 x 17

Step 4: Therefore, the least common multiple of 6069 and 6075 is 12289725.