Least Common Multiple of 1006 and 1014

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 1014 the smallest integer that is 510042 that is divisible by both numbers.

Least Common Multiple (LCM) of 1006 and 1014 is 510042.

LCM(1006,1014) = 510042

LCM of 1006 and 1014

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

LCM of:
and

Least Common Multiple of 1006 and 1014

LCM of 1006 and 1014 is 510042

Least common multiple can be found by multiplying the highest exponent prime factors of 1006 and 1014. First we will calculate the prime factors of 1006 and 1014.

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 1014


2 1014
3 507
13 169
13 13
1

Prime factors of 1014 are 2, 3,13. Prime factorization of 1014 in exponential form is:

1014 = 21×31×132

Now multiplying the highest exponent prime factors to calculate the LCM of 1006 and 1014.

LCM(1006,1014) = 21×31×132×5031
LCM(1006,1014) = 510042

Factors of 1006

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

1, 2, 503, 1006

Factors of 1014

List of positive integer factors of 1014 that divides 1014 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014

Least Common Multiple of 1006 and 1014 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 1014, than apply into the LCM equation.

GCF(1006,1014) = 2
LCM(1006,1014) = ( 1006 × 1014) / 2
LCM(1006,1014) = 1020084 / 2
LCM(1006,1014) = 510042

Properties of LCM 1006 and 1014

(i) The LCM of 1014 and 1006 is associative

LCM of 1006 and 1014 = LCM of 1014 and 1006

Related Least Common Multiples of 1006

Related Least Common Multiples of 1014

Frequently Asked Questions on LCM of 1006 and 1014

1. What is the LCM of 1006 and 1014?

Answer: LCM of 1006 and 1014 is 510042.

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 1014?

Answer: Factors of 1014 are 1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014. There are 12 integers that are factors of 1014. The greatest factor of 1014 is 1014.

4. How to Find the LCM of 1006 and 1014?

Answer:

Least Common Multiple of 1006 and 1014 = 510042

Step 1: Find the prime factorization of 1006

1006 = 2 x 503

Step 2: Find the prime factorization of 1014

1014 = 2 x 3 x 13 x 13

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

LCM = 510042 = 2 x 3 x 13 x 13 x 503

Step 4: Therefore, the least common multiple of 1006 and 1014 is 510042.