Least Common Multiple of 30004 and 30012

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 30004 and 30012 the smallest integer that is 225120012 that is divisible by both numbers.

Least Common Multiple (LCM) of 30004 and 30012 is 225120012.

LCM(30004,30012) = 225120012

LCM of 30004 and 30012

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

LCM of:
and

Least Common Multiple of 30004 and 30012

LCM of 30004 and 30012 is 225120012

Least common multiple can be found by multiplying the highest exponent prime factors of 30004 and 30012. First we will calculate the prime factors of 30004 and 30012.

Prime Factorization of 30004


2 30004
2 15002
13 7501
577 577
1

Prime factors of 30004 are 2, 13,577. Prime factorization of 30004 in exponential form is:

30004 = 22×131×5771

Prime Factorization of 30012


2 30012
2 15006
3 7503
41 2501
61 61
1

Prime factors of 30012 are 2, 3, 41,61. Prime factorization of 30012 in exponential form is:

30012 = 22×31×411×611

Now multiplying the highest exponent prime factors to calculate the LCM of 30004 and 30012.

LCM(30004,30012) = 22×31×131×411×611×5771
LCM(30004,30012) = 225120012

Factors of 30004

List of positive integer factors of 30004 that divides 30004 without a remainder.

1, 2, 4, 13, 26, 52, 577, 1154, 2308, 7501, 15002, 30004

Factors of 30012

List of positive integer factors of 30012 that divides 30012 without a remainder.

1, 2, 3, 4, 6, 12, 41, 61, 82, 122, 123, 164, 183, 244, 246, 366, 492, 732, 2501, 5002, 7503, 10004, 15006, 30012

Least Common Multiple of 30004 and 30012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30004 and 30012, than apply into the LCM equation.

GCF(30004,30012) = 4
LCM(30004,30012) = ( 30004 × 30012) / 4
LCM(30004,30012) = 900480048 / 4
LCM(30004,30012) = 225120012

Properties of LCM 30004 and 30012

(i) The LCM of 30012 and 30004 is associative

LCM of 30004 and 30012 = LCM of 30012 and 30004

Related Least Common Multiples of 30004

Related Least Common Multiples of 30012

Frequently Asked Questions on LCM of 30004 and 30012

1. What is the LCM of 30004 and 30012?

Answer: LCM of 30004 and 30012 is 225120012.

2. What are the Factors of 30004?

Answer: Factors of 30004 are 1, 2, 4, 13, 26, 52, 577, 1154, 2308, 7501, 15002, 30004. There are 12 integers that are factors of 30004. The greatest factor of 30004 is 30004.

3. What are the Factors of 30012?

Answer: Factors of 30012 are 1, 2, 3, 4, 6, 12, 41, 61, 82, 122, 123, 164, 183, 244, 246, 366, 492, 732, 2501, 5002, 7503, 10004, 15006, 30012. There are 24 integers that are factors of 30012. The greatest factor of 30012 is 30012.

4. How to Find the LCM of 30004 and 30012?

Answer:

Least Common Multiple of 30004 and 30012 = 225120012

Step 1: Find the prime factorization of 30004

30004 = 2 x 2 x 13 x 577

Step 2: Find the prime factorization of 30012

30012 = 2 x 2 x 3 x 41 x 61

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

LCM = 225120012 = 2 x 2 x 3 x 13 x 41 x 61 x 577

Step 4: Therefore, the least common multiple of 30004 and 30012 is 225120012.