Least Common Multiple of 30006 and 30010

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 30006 and 30010 the smallest integer that is 450240030 that is divisible by both numbers.

Least Common Multiple (LCM) of 30006 and 30010 is 450240030.

LCM(30006,30010) = 450240030

LCM of 30006 and 30010

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

LCM of:
and

Least Common Multiple of 30006 and 30010

LCM of 30006 and 30010 is 450240030

Least common multiple can be found by multiplying the highest exponent prime factors of 30006 and 30010. First we will calculate the prime factors of 30006 and 30010.

Prime Factorization of 30006


2 30006
3 15003
3 5001
1667 1667
1

Prime factors of 30006 are 2, 3,1667. Prime factorization of 30006 in exponential form is:

30006 = 21×32×16671

Prime Factorization of 30010


2 30010
5 15005
3001 3001
1

Prime factors of 30010 are 2, 5,3001. Prime factorization of 30010 in exponential form is:

30010 = 21×51×30011

Now multiplying the highest exponent prime factors to calculate the LCM of 30006 and 30010.

LCM(30006,30010) = 21×32×51×16671×30011
LCM(30006,30010) = 450240030

Factors of 30006

List of positive integer factors of 30006 that divides 30006 without a remainder.

1, 2, 3, 6, 9, 18, 1667, 3334, 5001, 10002, 15003, 30006

Factors of 30010

List of positive integer factors of 30010 that divides 30010 without a remainder.

1, 2, 5, 10, 3001, 6002, 15005, 30010

Least Common Multiple of 30006 and 30010 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30006 and 30010, than apply into the LCM equation.

GCF(30006,30010) = 2
LCM(30006,30010) = ( 30006 × 30010) / 2
LCM(30006,30010) = 900480060 / 2
LCM(30006,30010) = 450240030

Properties of LCM 30006 and 30010

(i) The LCM of 30010 and 30006 is associative

LCM of 30006 and 30010 = LCM of 30010 and 30006

Related Least Common Multiples of 30006

Related Least Common Multiples of 30010

Frequently Asked Questions on LCM of 30006 and 30010

1. What is the LCM of 30006 and 30010?

Answer: LCM of 30006 and 30010 is 450240030.

2. What are the Factors of 30006?

Answer: Factors of 30006 are 1, 2, 3, 6, 9, 18, 1667, 3334, 5001, 10002, 15003, 30006. There are 12 integers that are factors of 30006. The greatest factor of 30006 is 30006.

3. What are the Factors of 30010?

Answer: Factors of 30010 are 1, 2, 5, 10, 3001, 6002, 15005, 30010. There are 8 integers that are factors of 30010. The greatest factor of 30010 is 30010.

4. How to Find the LCM of 30006 and 30010?

Answer:

Least Common Multiple of 30006 and 30010 = 450240030

Step 1: Find the prime factorization of 30006

30006 = 2 x 3 x 3 x 1667

Step 2: Find the prime factorization of 30010

30010 = 2 x 5 x 3001

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

LCM = 450240030 = 2 x 3 x 3 x 5 x 1667 x 3001

Step 4: Therefore, the least common multiple of 30006 and 30010 is 450240030.