Least Common Multiple of 7000 and 7007

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 7007 the smallest integer that is 7007000 that is divisible by both numbers.

Least Common Multiple (LCM) of 7000 and 7007 is 7007000.

LCM(7000,7007) = 7007000

LCM of 7000 and 7007

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

LCM of:
and

Least Common Multiple of 7000 and 7007

LCM of 7000 and 7007 is 7007000

Least common multiple can be found by multiplying the highest exponent prime factors of 7000 and 7007. First we will calculate the prime factors of 7000 and 7007.

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 7007


7 7007
7 1001
11 143
13 13
1

Prime factors of 7007 are 7, 11,13. Prime factorization of 7007 in exponential form is:

7007 = 72×111×131

Now multiplying the highest exponent prime factors to calculate the LCM of 7000 and 7007.

LCM(7000,7007) = 23×53×72×111×131
LCM(7000,7007) = 7007000

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 7007

List of positive integer factors of 7007 that divides 7007 without a remainder.

1, 7, 11, 13, 49, 77, 91, 143, 539, 637, 1001, 7007

Least Common Multiple of 7000 and 7007 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 7007, than apply into the LCM equation.

GCF(7000,7007) = 7
LCM(7000,7007) = ( 7000 × 7007) / 7
LCM(7000,7007) = 49049000 / 7
LCM(7000,7007) = 7007000

Properties of LCM 7000 and 7007

(i) The LCM of 7007 and 7000 is associative

LCM of 7000 and 7007 = LCM of 7007 and 7000

Related Least Common Multiples of 7000

Related Least Common Multiples of 7007

Frequently Asked Questions on LCM of 7000 and 7007

1. What is the LCM of 7000 and 7007?

Answer: LCM of 7000 and 7007 is 7007000.

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 7007?

Answer: Factors of 7007 are 1, 7, 11, 13, 49, 77, 91, 143, 539, 637, 1001, 7007. There are 12 integers that are factors of 7007. The greatest factor of 7007 is 7007.

4. How to Find the LCM of 7000 and 7007?

Answer:

Least Common Multiple of 7000 and 7007 = 7007000

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 7007

7007 = 7 x 7 x 11 x 13

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

LCM = 7007000 = 2 x 2 x 2 x 5 x 5 x 5 x 7 x 7 x 11 x 13

Step 4: Therefore, the least common multiple of 7000 and 7007 is 7007000.