Least Common Multiple of 1004 and 1007

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1004 and 1007 the smallest integer that is 1011028 that is divisible by both numbers.

Least Common Multiple (LCM) of 1004 and 1007 is 1011028.

LCM(1004,1007) = 1011028

LCM of 1004 and 1007

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

LCM of:
and

Least Common Multiple of 1004 and 1007

LCM of 1004 and 1007 is 1011028

Least common multiple can be found by multiplying the highest exponent prime factors of 1004 and 1007. First we will calculate the prime factors of 1004 and 1007.

Prime Factorization of 1004


2 1004
2 502
251 251
1

Prime factors of 1004 are 2,251. Prime factorization of 1004 in exponential form is:

1004 = 22×2511

Prime Factorization of 1007


19 1007
53 53
1

Prime factors of 1007 are 19,53. Prime factorization of 1007 in exponential form is:

1007 = 191×531

Now multiplying the highest exponent prime factors to calculate the LCM of 1004 and 1007.

LCM(1004,1007) = 22×191×531×2511
LCM(1004,1007) = 1011028

Factors of 1004

List of positive integer factors of 1004 that divides 1004 without a remainder.

1, 2, 4, 251, 502, 1004

Factors of 1007

List of positive integer factors of 1007 that divides 1007 without a remainder.

1, 19, 53, 1007

Least Common Multiple of 1004 and 1007 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1004 and 1007, than apply into the LCM equation.

GCF(1004,1007) = 1
LCM(1004,1007) = ( 1004 × 1007) / 1
LCM(1004,1007) = 1011028 / 1
LCM(1004,1007) = 1011028

Properties of LCM 1004 and 1007

(i) The LCM of 1007 and 1004 is associative

LCM of 1004 and 1007 = LCM of 1007 and 1004

Related Least Common Multiples of 1004

Related Least Common Multiples of 1007

Frequently Asked Questions on LCM of 1004 and 1007

1. What is the LCM of 1004 and 1007?

Answer: LCM of 1004 and 1007 is 1011028.

2. What are the Factors of 1004?

Answer: Factors of 1004 are 1, 2, 4, 251, 502, 1004. There are 6 integers that are factors of 1004. The greatest factor of 1004 is 1004.

3. What are the Factors of 1007?

Answer: Factors of 1007 are 1, 19, 53, 1007. There are 4 integers that are factors of 1007. The greatest factor of 1007 is 1007.

4. How to Find the LCM of 1004 and 1007?

Answer:

Least Common Multiple of 1004 and 1007 = 1011028

Step 1: Find the prime factorization of 1004

1004 = 2 x 2 x 251

Step 2: Find the prime factorization of 1007

1007 = 19 x 53

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

LCM = 1011028 = 2 x 2 x 19 x 53 x 251

Step 4: Therefore, the least common multiple of 1004 and 1007 is 1011028.