Least Common Multiple of 7000 and 7006

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 7006 the smallest integer that is 24521000 that is divisible by both numbers.

Least Common Multiple (LCM) of 7000 and 7006 is 24521000.

LCM(7000,7006) = 24521000

LCM of 7000 and 7006

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

LCM of:
and

Least Common Multiple of 7000 and 7006

LCM of 7000 and 7006 is 24521000

Least common multiple can be found by multiplying the highest exponent prime factors of 7000 and 7006. First we will calculate the prime factors of 7000 and 7006.

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 7006


2 7006
31 3503
113 113
1

Prime factors of 7006 are 2, 31,113. Prime factorization of 7006 in exponential form is:

7006 = 21×311×1131

Now multiplying the highest exponent prime factors to calculate the LCM of 7000 and 7006.

LCM(7000,7006) = 23×53×71×311×1131
LCM(7000,7006) = 24521000

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 7006

List of positive integer factors of 7006 that divides 7006 without a remainder.

1, 2, 31, 62, 113, 226, 3503, 7006

Least Common Multiple of 7000 and 7006 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 7006, than apply into the LCM equation.

GCF(7000,7006) = 2
LCM(7000,7006) = ( 7000 × 7006) / 2
LCM(7000,7006) = 49042000 / 2
LCM(7000,7006) = 24521000

Properties of LCM 7000 and 7006

(i) The LCM of 7006 and 7000 is associative

LCM of 7000 and 7006 = LCM of 7006 and 7000

Related Least Common Multiples of 7000

Related Least Common Multiples of 7006

Frequently Asked Questions on LCM of 7000 and 7006

1. What is the LCM of 7000 and 7006?

Answer: LCM of 7000 and 7006 is 24521000.

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 7006?

Answer: Factors of 7006 are 1, 2, 31, 62, 113, 226, 3503, 7006. There are 8 integers that are factors of 7006. The greatest factor of 7006 is 7006.

4. How to Find the LCM of 7000 and 7006?

Answer:

Least Common Multiple of 7000 and 7006 = 24521000

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 7006

7006 = 2 x 31 x 113

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

LCM = 24521000 = 2 x 2 x 2 x 5 x 5 x 5 x 7 x 31 x 113

Step 4: Therefore, the least common multiple of 7000 and 7006 is 24521000.