Least Common Multiple of 3000 and 3008

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3000 and 3008 the smallest integer that is 1128000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3000 and 3008 is 1128000.

LCM(3000,3008) = 1128000

LCM of 3000 and 3008

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

LCM of:
and

Least Common Multiple of 3000 and 3008

LCM of 3000 and 3008 is 1128000

Least common multiple can be found by multiplying the highest exponent prime factors of 3000 and 3008. First we will calculate the prime factors of 3000 and 3008.

Prime Factorization of 3000


2 3000
2 1500
2 750
3 375
5 125
5 25
5 5
1

Prime factors of 3000 are 2, 3,5. Prime factorization of 3000 in exponential form is:

3000 = 23×31×53

Prime Factorization of 3008


2 3008
2 1504
2 752
2 376
2 188
2 94
47 47
1

Prime factors of 3008 are 2,47. Prime factorization of 3008 in exponential form is:

3008 = 26×471

Now multiplying the highest exponent prime factors to calculate the LCM of 3000 and 3008.

LCM(3000,3008) = 26×31×53×471
LCM(3000,3008) = 1128000

Factors of 3000

List of positive integer factors of 3000 that divides 3000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000

Factors of 3008

List of positive integer factors of 3008 that divides 3008 without a remainder.

1, 2, 4, 8, 16, 32, 47, 64, 94, 188, 376, 752, 1504, 3008

Least Common Multiple of 3000 and 3008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3000 and 3008, than apply into the LCM equation.

GCF(3000,3008) = 8
LCM(3000,3008) = ( 3000 × 3008) / 8
LCM(3000,3008) = 9024000 / 8
LCM(3000,3008) = 1128000

Properties of LCM 3000 and 3008

(i) The LCM of 3008 and 3000 is associative

LCM of 3000 and 3008 = LCM of 3008 and 3000

Related Least Common Multiples of 3000

Related Least Common Multiples of 3008

Frequently Asked Questions on LCM of 3000 and 3008

1. What is the LCM of 3000 and 3008?

Answer: LCM of 3000 and 3008 is 1128000.

2. What are the Factors of 3000?

Answer: Factors of 3000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000. There are 32 integers that are factors of 3000. The greatest factor of 3000 is 3000.

3. What are the Factors of 3008?

Answer: Factors of 3008 are 1, 2, 4, 8, 16, 32, 47, 64, 94, 188, 376, 752, 1504, 3008. There are 14 integers that are factors of 3008. The greatest factor of 3008 is 3008.

4. How to Find the LCM of 3000 and 3008?

Answer:

Least Common Multiple of 3000 and 3008 = 1128000

Step 1: Find the prime factorization of 3000

3000 = 2 x 2 x 2 x 3 x 5 x 5 x 5

Step 2: Find the prime factorization of 3008

3008 = 2 x 2 x 2 x 2 x 2 x 2 x 47

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

LCM = 1128000 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 47

Step 4: Therefore, the least common multiple of 3000 and 3008 is 1128000.