Least Common Multiple of 1006 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 1006 and 1007 the smallest integer that is 1013042 that is divisible by both numbers.

Least Common Multiple (LCM) of 1006 and 1007 is 1013042.

LCM(1006,1007) = 1013042

LCM of 1006 and 1007

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

LCM of:
and

Least Common Multiple of 1006 and 1007

LCM of 1006 and 1007 is 1013042

Least common multiple can be found by multiplying the highest exponent prime factors of 1006 and 1007. First we will calculate the prime factors of 1006 and 1007.

Prime Factorization of 1006


2 1006
503 503
1

Prime factors of 1006 are 2,503. Prime factorization of 1006 in exponential form is:

1006 = 21×5031

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 1006 and 1007.

LCM(1006,1007) = 21×191×531×5031
LCM(1006,1007) = 1013042

Factors of 1006

List of positive integer factors of 1006 that divides 1006 without a remainder.

1, 2, 503, 1006

Factors of 1007

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

1, 19, 53, 1007

Least Common Multiple of 1006 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 1006 and 1007, than apply into the LCM equation.

GCF(1006,1007) = 1
LCM(1006,1007) = ( 1006 × 1007) / 1
LCM(1006,1007) = 1013042 / 1
LCM(1006,1007) = 1013042

Properties of LCM 1006 and 1007

(i) The LCM of 1007 and 1006 is associative

LCM of 1006 and 1007 = LCM of 1007 and 1006

Related Least Common Multiples of 1006

Related Least Common Multiples of 1007

Frequently Asked Questions on LCM of 1006 and 1007

1. What is the LCM of 1006 and 1007?

Answer: LCM of 1006 and 1007 is 1013042.

2. What are the Factors of 1006?

Answer: Factors of 1006 are 1, 2, 503, 1006. There are 4 integers that are factors of 1006. The greatest factor of 1006 is 1006.

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 1006 and 1007?

Answer:

Least Common Multiple of 1006 and 1007 = 1013042

Step 1: Find the prime factorization of 1006

1006 = 2 x 503

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 = 1013042 = 2 x 19 x 53 x 503

Step 4: Therefore, the least common multiple of 1006 and 1007 is 1013042.