Least Common Multiple of 30000 and 30002

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 30000 and 30002 the smallest integer that is 450030000 that is divisible by both numbers.

Least Common Multiple (LCM) of 30000 and 30002 is 450030000.

LCM(30000,30002) = 450030000

LCM of 30000 and 30002

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

LCM of:
and

Least Common Multiple of 30000 and 30002

LCM of 30000 and 30002 is 450030000

Least common multiple can be found by multiplying the highest exponent prime factors of 30000 and 30002. First we will calculate the prime factors of 30000 and 30002.

Prime Factorization of 30000


2 30000
2 15000
2 7500
2 3750
3 1875
5 625
5 125
5 25
5 5
1

Prime factors of 30000 are 2, 3,5. Prime factorization of 30000 in exponential form is:

30000 = 24×31×54

Prime Factorization of 30002


2 30002
7 15001
2143 2143
1

Prime factors of 30002 are 2, 7,2143. Prime factorization of 30002 in exponential form is:

30002 = 21×71×21431

Now multiplying the highest exponent prime factors to calculate the LCM of 30000 and 30002.

LCM(30000,30002) = 24×31×54×71×21431
LCM(30000,30002) = 450030000

Factors of 30000

List of positive integer factors of 30000 that divides 30000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 625, 750, 1000, 1200, 1250, 1500, 1875, 2000, 2500, 3000, 3750, 5000, 6000, 7500, 10000, 15000, 30000

Factors of 30002

List of positive integer factors of 30002 that divides 30002 without a remainder.

1, 2, 7, 14, 2143, 4286, 15001, 30002

Least Common Multiple of 30000 and 30002 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30000 and 30002, than apply into the LCM equation.

GCF(30000,30002) = 2
LCM(30000,30002) = ( 30000 × 30002) / 2
LCM(30000,30002) = 900060000 / 2
LCM(30000,30002) = 450030000

Properties of LCM 30000 and 30002

(i) The LCM of 30002 and 30000 is associative

LCM of 30000 and 30002 = LCM of 30002 and 30000

Related Least Common Multiples of 30000

Related Least Common Multiples of 30002

Frequently Asked Questions on LCM of 30000 and 30002

1. What is the LCM of 30000 and 30002?

Answer: LCM of 30000 and 30002 is 450030000.

2. What are the Factors of 30000?

Answer: Factors of 30000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 625, 750, 1000, 1200, 1250, 1500, 1875, 2000, 2500, 3000, 3750, 5000, 6000, 7500, 10000, 15000, 30000. There are 50 integers that are factors of 30000. The greatest factor of 30000 is 30000.

3. What are the Factors of 30002?

Answer: Factors of 30002 are 1, 2, 7, 14, 2143, 4286, 15001, 30002. There are 8 integers that are factors of 30002. The greatest factor of 30002 is 30002.

4. How to Find the LCM of 30000 and 30002?

Answer:

Least Common Multiple of 30000 and 30002 = 450030000

Step 1: Find the prime factorization of 30000

30000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5

Step 2: Find the prime factorization of 30002

30002 = 2 x 7 x 2143

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

LCM = 450030000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5 x 7 x 2143

Step 4: Therefore, the least common multiple of 30000 and 30002 is 450030000.