Least Common Multiple of 7000 and 7004

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 7004 the smallest integer that is 12257000 that is divisible by both numbers.

Least Common Multiple (LCM) of 7000 and 7004 is 12257000.

LCM(7000,7004) = 12257000

LCM of 7000 and 7004

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

LCM of:
and

Least Common Multiple of 7000 and 7004

LCM of 7000 and 7004 is 12257000

Least common multiple can be found by multiplying the highest exponent prime factors of 7000 and 7004. First we will calculate the prime factors of 7000 and 7004.

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 7004


2 7004
2 3502
17 1751
103 103
1

Prime factors of 7004 are 2, 17,103. Prime factorization of 7004 in exponential form is:

7004 = 22×171×1031

Now multiplying the highest exponent prime factors to calculate the LCM of 7000 and 7004.

LCM(7000,7004) = 23×53×71×171×1031
LCM(7000,7004) = 12257000

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 7004

List of positive integer factors of 7004 that divides 7004 without a remainder.

1, 2, 4, 17, 34, 68, 103, 206, 412, 1751, 3502, 7004

Least Common Multiple of 7000 and 7004 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 7004, than apply into the LCM equation.

GCF(7000,7004) = 4
LCM(7000,7004) = ( 7000 × 7004) / 4
LCM(7000,7004) = 49028000 / 4
LCM(7000,7004) = 12257000

Properties of LCM 7000 and 7004

(i) The LCM of 7004 and 7000 is associative

LCM of 7000 and 7004 = LCM of 7004 and 7000

Related Least Common Multiples of 7000

Related Least Common Multiples of 7004

Frequently Asked Questions on LCM of 7000 and 7004

1. What is the LCM of 7000 and 7004?

Answer: LCM of 7000 and 7004 is 12257000.

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 7004?

Answer: Factors of 7004 are 1, 2, 4, 17, 34, 68, 103, 206, 412, 1751, 3502, 7004. There are 12 integers that are factors of 7004. The greatest factor of 7004 is 7004.

4. How to Find the LCM of 7000 and 7004?

Answer:

Least Common Multiple of 7000 and 7004 = 12257000

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 7004

7004 = 2 x 2 x 17 x 103

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

LCM = 12257000 = 2 x 2 x 2 x 5 x 5 x 5 x 7 x 17 x 103

Step 4: Therefore, the least common multiple of 7000 and 7004 is 12257000.