Least Common Multiple of 6045 and 6048

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6045 and 6048 the smallest integer that is 12186720 that is divisible by both numbers.

Least Common Multiple (LCM) of 6045 and 6048 is 12186720.

LCM(6045,6048) = 12186720

LCM of 6045 and 6048

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

LCM of:
and

Least Common Multiple of 6045 and 6048

LCM of 6045 and 6048 is 12186720

Least common multiple can be found by multiplying the highest exponent prime factors of 6045 and 6048. First we will calculate the prime factors of 6045 and 6048.

Prime Factorization of 6045


3 6045
5 2015
13 403
31 31
1

Prime factors of 6045 are 3, 5, 13,31. Prime factorization of 6045 in exponential form is:

6045 = 31×51×131×311

Prime Factorization of 6048


2 6048
2 3024
2 1512
2 756
2 378
3 189
3 63
3 21
7 7
1

Prime factors of 6048 are 2, 3,7. Prime factorization of 6048 in exponential form is:

6048 = 25×33×71

Now multiplying the highest exponent prime factors to calculate the LCM of 6045 and 6048.

LCM(6045,6048) = 25×33×51×71×131×311
LCM(6045,6048) = 12186720

Factors of 6045

List of positive integer factors of 6045 that divides 6045 without a remainder.

1, 3, 5, 13, 15, 31, 39, 65, 93, 155, 195, 403, 465, 1209, 2015, 6045

Factors of 6048

List of positive integer factors of 6048 that divides 6048 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 72, 84, 96, 108, 112, 126, 144, 168, 189, 216, 224, 252, 288, 336, 378, 432, 504, 672, 756, 864, 1008, 1512, 2016, 3024, 6048

Least Common Multiple of 6045 and 6048 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6045 and 6048, than apply into the LCM equation.

GCF(6045,6048) = 3
LCM(6045,6048) = ( 6045 × 6048) / 3
LCM(6045,6048) = 36560160 / 3
LCM(6045,6048) = 12186720

Properties of LCM 6045 and 6048

(i) The LCM of 6048 and 6045 is associative

LCM of 6045 and 6048 = LCM of 6048 and 6045

Related Least Common Multiples of 6045

Related Least Common Multiples of 6048

Frequently Asked Questions on LCM of 6045 and 6048

1. What is the LCM of 6045 and 6048?

Answer: LCM of 6045 and 6048 is 12186720.

2. What are the Factors of 6045?

Answer: Factors of 6045 are 1, 3, 5, 13, 15, 31, 39, 65, 93, 155, 195, 403, 465, 1209, 2015, 6045. There are 16 integers that are factors of 6045. The greatest factor of 6045 is 6045.

3. What are the Factors of 6048?

Answer: Factors of 6048 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 72, 84, 96, 108, 112, 126, 144, 168, 189, 216, 224, 252, 288, 336, 378, 432, 504, 672, 756, 864, 1008, 1512, 2016, 3024, 6048. There are 48 integers that are factors of 6048. The greatest factor of 6048 is 6048.

4. How to Find the LCM of 6045 and 6048?

Answer:

Least Common Multiple of 6045 and 6048 = 12186720

Step 1: Find the prime factorization of 6045

6045 = 3 x 5 x 13 x 31

Step 2: Find the prime factorization of 6048

6048 = 2 x 2 x 2 x 2 x 2 x 3 x 3 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 = 12186720 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7 x 13 x 31

Step 4: Therefore, the least common multiple of 6045 and 6048 is 12186720.