Least Common Multiple of 6744 and 6750

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6744 and 6750 the smallest integer that is 7587000 that is divisible by both numbers.

Least Common Multiple (LCM) of 6744 and 6750 is 7587000.

LCM(6744,6750) = 7587000

LCM of 6744 and 6750

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

LCM of:
and

Least Common Multiple of 6744 and 6750

LCM of 6744 and 6750 is 7587000

Least common multiple can be found by multiplying the highest exponent prime factors of 6744 and 6750. First we will calculate the prime factors of 6744 and 6750.

Prime Factorization of 6744


2 6744
2 3372
2 1686
3 843
281 281
1

Prime factors of 6744 are 2, 3,281. Prime factorization of 6744 in exponential form is:

6744 = 23×31×2811

Prime Factorization of 6750


2 6750
3 3375
3 1125
3 375
5 125
5 25
5 5
1

Prime factors of 6750 are 2, 3,5. Prime factorization of 6750 in exponential form is:

6750 = 21×33×53

Now multiplying the highest exponent prime factors to calculate the LCM of 6744 and 6750.

LCM(6744,6750) = 23×33×53×2811
LCM(6744,6750) = 7587000

Factors of 6744

List of positive integer factors of 6744 that divides 6744 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 281, 562, 843, 1124, 1686, 2248, 3372, 6744

Factors of 6750

List of positive integer factors of 6750 that divides 6750 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 125, 135, 150, 225, 250, 270, 375, 450, 675, 750, 1125, 1350, 2250, 3375, 6750

Least Common Multiple of 6744 and 6750 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6744 and 6750, than apply into the LCM equation.

GCF(6744,6750) = 6
LCM(6744,6750) = ( 6744 × 6750) / 6
LCM(6744,6750) = 45522000 / 6
LCM(6744,6750) = 7587000

Properties of LCM 6744 and 6750

(i) The LCM of 6750 and 6744 is associative

LCM of 6744 and 6750 = LCM of 6750 and 6744

Related Least Common Multiples of 6744

Related Least Common Multiples of 6750

Frequently Asked Questions on LCM of 6744 and 6750

1. What is the LCM of 6744 and 6750?

Answer: LCM of 6744 and 6750 is 7587000.

2. What are the Factors of 6744?

Answer: Factors of 6744 are 1, 2, 3, 4, 6, 8, 12, 24, 281, 562, 843, 1124, 1686, 2248, 3372, 6744. There are 16 integers that are factors of 6744. The greatest factor of 6744 is 6744.

3. What are the Factors of 6750?

Answer: Factors of 6750 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 125, 135, 150, 225, 250, 270, 375, 450, 675, 750, 1125, 1350, 2250, 3375, 6750. There are 32 integers that are factors of 6750. The greatest factor of 6750 is 6750.

4. How to Find the LCM of 6744 and 6750?

Answer:

Least Common Multiple of 6744 and 6750 = 7587000

Step 1: Find the prime factorization of 6744

6744 = 2 x 2 x 2 x 3 x 281

Step 2: Find the prime factorization of 6750

6750 = 2 x 3 x 3 x 3 x 5 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 = 7587000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5 x 281

Step 4: Therefore, the least common multiple of 6744 and 6750 is 7587000.