Least Common Multiple of 6138 and 6144

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6138 and 6144 the smallest integer that is 6285312 that is divisible by both numbers.

Least Common Multiple (LCM) of 6138 and 6144 is 6285312.

LCM(6138,6144) = 6285312

LCM of 6138 and 6144

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

LCM of:
and

Least Common Multiple of 6138 and 6144

LCM of 6138 and 6144 is 6285312

Least common multiple can be found by multiplying the highest exponent prime factors of 6138 and 6144. First we will calculate the prime factors of 6138 and 6144.

Prime Factorization of 6138


2 6138
3 3069
3 1023
11 341
31 31
1

Prime factors of 6138 are 2, 3, 11,31. Prime factorization of 6138 in exponential form is:

6138 = 21×32×111×311

Prime Factorization of 6144


2 6144
2 3072
2 1536
2 768
2 384
2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 6144 are 2,3. Prime factorization of 6144 in exponential form is:

6144 = 211×31

Now multiplying the highest exponent prime factors to calculate the LCM of 6138 and 6144.

LCM(6138,6144) = 211×32×111×311
LCM(6138,6144) = 6285312

Factors of 6138

List of positive integer factors of 6138 that divides 6138 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 31, 33, 62, 66, 93, 99, 186, 198, 279, 341, 558, 682, 1023, 2046, 3069, 6138

Factors of 6144

List of positive integer factors of 6144 that divides 6144 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 6144

Least Common Multiple of 6138 and 6144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6138 and 6144, than apply into the LCM equation.

GCF(6138,6144) = 6
LCM(6138,6144) = ( 6138 × 6144) / 6
LCM(6138,6144) = 37711872 / 6
LCM(6138,6144) = 6285312

Properties of LCM 6138 and 6144

(i) The LCM of 6144 and 6138 is associative

LCM of 6138 and 6144 = LCM of 6144 and 6138

Related Least Common Multiples of 6138

Related Least Common Multiples of 6144

Frequently Asked Questions on LCM of 6138 and 6144

1. What is the LCM of 6138 and 6144?

Answer: LCM of 6138 and 6144 is 6285312.

2. What are the Factors of 6138?

Answer: Factors of 6138 are 1, 2, 3, 6, 9, 11, 18, 22, 31, 33, 62, 66, 93, 99, 186, 198, 279, 341, 558, 682, 1023, 2046, 3069, 6138. There are 24 integers that are factors of 6138. The greatest factor of 6138 is 6138.

3. What are the Factors of 6144?

Answer: Factors of 6144 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 6144. There are 24 integers that are factors of 6144. The greatest factor of 6144 is 6144.

4. How to Find the LCM of 6138 and 6144?

Answer:

Least Common Multiple of 6138 and 6144 = 6285312

Step 1: Find the prime factorization of 6138

6138 = 2 x 3 x 3 x 11 x 31

Step 2: Find the prime factorization of 6144

6144 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

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

LCM = 6285312 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 11 x 31

Step 4: Therefore, the least common multiple of 6138 and 6144 is 6285312.