Least Common Multiple of 7000 and 7005

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7000 and 7005 the smallest integer that is 9807000 that is divisible by both numbers.

Least Common Multiple (LCM) of 7000 and 7005 is 9807000.

LCM(7000,7005) = 9807000

LCM of 7000 and 7005

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

LCM of:
and

Least Common Multiple of 7000 and 7005

LCM of 7000 and 7005 is 9807000

Least common multiple can be found by multiplying the highest exponent prime factors of 7000 and 7005. First we will calculate the prime factors of 7000 and 7005.

Prime Factorization of 7000


2 7000
2 3500
2 1750
5 875
5 175
5 35
7 7
1

Prime factors of 7000 are 2, 5,7. Prime factorization of 7000 in exponential form is:

7000 = 23×53×71

Prime Factorization of 7005


3 7005
5 2335
467 467
1

Prime factors of 7005 are 3, 5,467. Prime factorization of 7005 in exponential form is:

7005 = 31×51×4671

Now multiplying the highest exponent prime factors to calculate the LCM of 7000 and 7005.

LCM(7000,7005) = 23×31×53×71×4671
LCM(7000,7005) = 9807000

Factors of 7000

List of positive integer factors of 7000 that divides 7000 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000

Factors of 7005

List of positive integer factors of 7005 that divides 7005 without a remainder.

1, 3, 5, 15, 467, 1401, 2335, 7005

Least Common Multiple of 7000 and 7005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7000 and 7005, than apply into the LCM equation.

GCF(7000,7005) = 5
LCM(7000,7005) = ( 7000 × 7005) / 5
LCM(7000,7005) = 49035000 / 5
LCM(7000,7005) = 9807000

Properties of LCM 7000 and 7005

(i) The LCM of 7005 and 7000 is associative

LCM of 7000 and 7005 = LCM of 7005 and 7000

Related Least Common Multiples of 7000

Related Least Common Multiples of 7005

Frequently Asked Questions on LCM of 7000 and 7005

1. What is the LCM of 7000 and 7005?

Answer: LCM of 7000 and 7005 is 9807000.

2. What are the Factors of 7000?

Answer: Factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000. There are 32 integers that are factors of 7000. The greatest factor of 7000 is 7000.

3. What are the Factors of 7005?

Answer: Factors of 7005 are 1, 3, 5, 15, 467, 1401, 2335, 7005. There are 8 integers that are factors of 7005. The greatest factor of 7005 is 7005.

4. How to Find the LCM of 7000 and 7005?

Answer:

Least Common Multiple of 7000 and 7005 = 9807000

Step 1: Find the prime factorization of 7000

7000 = 2 x 2 x 2 x 5 x 5 x 5 x 7

Step 2: Find the prime factorization of 7005

7005 = 3 x 5 x 467

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

LCM = 9807000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 7 x 467

Step 4: Therefore, the least common multiple of 7000 and 7005 is 9807000.