Least Common Multiple of 6996 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 6996 and 7004 the smallest integer that is 12249996 that is divisible by both numbers.

Least Common Multiple (LCM) of 6996 and 7004 is 12249996.

LCM(6996,7004) = 12249996

LCM of 6996 and 7004

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

LCM of:
and

Least Common Multiple of 6996 and 7004

LCM of 6996 and 7004 is 12249996

Least common multiple can be found by multiplying the highest exponent prime factors of 6996 and 7004. First we will calculate the prime factors of 6996 and 7004.

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 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 6996 and 7004.

LCM(6996,7004) = 22×31×111×171×531×1031
LCM(6996,7004) = 12249996

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 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 6996 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 6996 and 7004, than apply into the LCM equation.

GCF(6996,7004) = 4
LCM(6996,7004) = ( 6996 × 7004) / 4
LCM(6996,7004) = 48999984 / 4
LCM(6996,7004) = 12249996

Properties of LCM 6996 and 7004

(i) The LCM of 7004 and 6996 is associative

LCM of 6996 and 7004 = LCM of 7004 and 6996

Related Least Common Multiples of 6996

Related Least Common Multiples of 7004

Frequently Asked Questions on LCM of 6996 and 7004

1. What is the LCM of 6996 and 7004?

Answer: LCM of 6996 and 7004 is 12249996.

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 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 6996 and 7004?

Answer:

Least Common Multiple of 6996 and 7004 = 12249996

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 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 = 12249996 = 2 x 2 x 3 x 11 x 17 x 53 x 103

Step 4: Therefore, the least common multiple of 6996 and 7004 is 12249996.