Least Common Multiple of 3000 and 3002

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 3002 the smallest integer that is 4503000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3000 and 3002 is 4503000.

LCM(3000,3002) = 4503000

LCM of 3000 and 3002

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

LCM of:
and

Least Common Multiple of 3000 and 3002

LCM of 3000 and 3002 is 4503000

Least common multiple can be found by multiplying the highest exponent prime factors of 3000 and 3002. First we will calculate the prime factors of 3000 and 3002.

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 3002


2 3002
19 1501
79 79
1

Prime factors of 3002 are 2, 19,79. Prime factorization of 3002 in exponential form is:

3002 = 21×191×791

Now multiplying the highest exponent prime factors to calculate the LCM of 3000 and 3002.

LCM(3000,3002) = 23×31×53×191×791
LCM(3000,3002) = 4503000

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 3002

List of positive integer factors of 3002 that divides 3002 without a remainder.

1, 2, 19, 38, 79, 158, 1501, 3002

Least Common Multiple of 3000 and 3002 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 3002, than apply into the LCM equation.

GCF(3000,3002) = 2
LCM(3000,3002) = ( 3000 × 3002) / 2
LCM(3000,3002) = 9006000 / 2
LCM(3000,3002) = 4503000

Properties of LCM 3000 and 3002

(i) The LCM of 3002 and 3000 is associative

LCM of 3000 and 3002 = LCM of 3002 and 3000

Related Least Common Multiples of 3000

Related Least Common Multiples of 3002

Frequently Asked Questions on LCM of 3000 and 3002

1. What is the LCM of 3000 and 3002?

Answer: LCM of 3000 and 3002 is 4503000.

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 3002?

Answer: Factors of 3002 are 1, 2, 19, 38, 79, 158, 1501, 3002. There are 8 integers that are factors of 3002. The greatest factor of 3002 is 3002.

4. How to Find the LCM of 3000 and 3002?

Answer:

Least Common Multiple of 3000 and 3002 = 4503000

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 3002

3002 = 2 x 19 x 79

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

LCM = 4503000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 19 x 79

Step 4: Therefore, the least common multiple of 3000 and 3002 is 4503000.