Least Common Multiple of 6996 and 7000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6996 and 7000 the smallest integer that is 12243000 that is divisible by both numbers.

Least Common Multiple (LCM) of 6996 and 7000 is 12243000.

LCM(6996,7000) = 12243000

LCM of 6996 and 7000

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

LCM of:
and

Least Common Multiple of 6996 and 7000

LCM of 6996 and 7000 is 12243000

Least common multiple can be found by multiplying the highest exponent prime factors of 6996 and 7000. First we will calculate the prime factors of 6996 and 7000.

Prime Factorization of 6996


2 6996
2 3498
3 1749
11 583
53 53
1

Prime factors of 6996 are 2, 3, 11,53. Prime factorization of 6996 in exponential form is:

6996 = 22×31×111×531

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

Now multiplying the highest exponent prime factors to calculate the LCM of 6996 and 7000.

LCM(6996,7000) = 23×31×53×71×111×531
LCM(6996,7000) = 12243000

Factors of 6996

List of positive integer factors of 6996 that divides 6996 without a remainder.

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 53, 66, 106, 132, 159, 212, 318, 583, 636, 1166, 1749, 2332, 3498, 6996

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

Least Common Multiple of 6996 and 7000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6996 and 7000, than apply into the LCM equation.

GCF(6996,7000) = 4
LCM(6996,7000) = ( 6996 × 7000) / 4
LCM(6996,7000) = 48972000 / 4
LCM(6996,7000) = 12243000

Properties of LCM 6996 and 7000

(i) The LCM of 7000 and 6996 is associative

LCM of 6996 and 7000 = LCM of 7000 and 6996

Related Least Common Multiples of 6996

Related Least Common Multiples of 7000

Frequently Asked Questions on LCM of 6996 and 7000

1. What is the LCM of 6996 and 7000?

Answer: LCM of 6996 and 7000 is 12243000.

2. What are the Factors of 6996?

Answer: Factors of 6996 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 53, 66, 106, 132, 159, 212, 318, 583, 636, 1166, 1749, 2332, 3498, 6996. There are 24 integers that are factors of 6996. The greatest factor of 6996 is 6996.

3. 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.

4. How to Find the LCM of 6996 and 7000?

Answer:

Least Common Multiple of 6996 and 7000 = 12243000

Step 1: Find the prime factorization of 6996

6996 = 2 x 2 x 3 x 11 x 53

Step 2: Find the prime factorization of 7000

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

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

LCM = 12243000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 7 x 11 x 53

Step 4: Therefore, the least common multiple of 6996 and 7000 is 12243000.