Least Common Multiple of 7000 and 7008

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 7008 the smallest integer that is 6132000 that is divisible by both numbers.

Least Common Multiple (LCM) of 7000 and 7008 is 6132000.

LCM(7000,7008) = 6132000

LCM of 7000 and 7008

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

LCM of:
and

Least Common Multiple of 7000 and 7008

LCM of 7000 and 7008 is 6132000

Least common multiple can be found by multiplying the highest exponent prime factors of 7000 and 7008. First we will calculate the prime factors of 7000 and 7008.

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 7008


2 7008
2 3504
2 1752
2 876
2 438
3 219
73 73
1

Prime factors of 7008 are 2, 3,73. Prime factorization of 7008 in exponential form is:

7008 = 25×31×731

Now multiplying the highest exponent prime factors to calculate the LCM of 7000 and 7008.

LCM(7000,7008) = 25×31×53×71×731
LCM(7000,7008) = 6132000

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 7008

List of positive integer factors of 7008 that divides 7008 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 73, 96, 146, 219, 292, 438, 584, 876, 1168, 1752, 2336, 3504, 7008

Least Common Multiple of 7000 and 7008 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 7008, than apply into the LCM equation.

GCF(7000,7008) = 8
LCM(7000,7008) = ( 7000 × 7008) / 8
LCM(7000,7008) = 49056000 / 8
LCM(7000,7008) = 6132000

Properties of LCM 7000 and 7008

(i) The LCM of 7008 and 7000 is associative

LCM of 7000 and 7008 = LCM of 7008 and 7000

Related Least Common Multiples of 7000

Related Least Common Multiples of 7008

Frequently Asked Questions on LCM of 7000 and 7008

1. What is the LCM of 7000 and 7008?

Answer: LCM of 7000 and 7008 is 6132000.

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 7008?

Answer: Factors of 7008 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 73, 96, 146, 219, 292, 438, 584, 876, 1168, 1752, 2336, 3504, 7008. There are 24 integers that are factors of 7008. The greatest factor of 7008 is 7008.

4. How to Find the LCM of 7000 and 7008?

Answer:

Least Common Multiple of 7000 and 7008 = 6132000

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 7008

7008 = 2 x 2 x 2 x 2 x 2 x 3 x 73

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

LCM = 6132000 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 7 x 73

Step 4: Therefore, the least common multiple of 7000 and 7008 is 6132000.