Least Common Multiple of 1008 and 1009

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1008 and 1009 the smallest integer that is 1017072 that is divisible by both numbers.

Least Common Multiple (LCM) of 1008 and 1009 is 1017072.

LCM(1008,1009) = 1017072

LCM of 1008 and 1009

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

LCM of:
and

Least Common Multiple of 1008 and 1009

LCM of 1008 and 1009 is 1017072

Least common multiple can be found by multiplying the highest exponent prime factors of 1008 and 1009. First we will calculate the prime factors of 1008 and 1009.

Prime Factorization of 1008


2 1008
2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 1008 are 2, 3,7. Prime factorization of 1008 in exponential form is:

1008 = 24×32×71

Prime Factorization of 1009


1009 1009
1

Prime factors of 1009 are 1009. Prime factorization of 1009 in exponential form is:

1009 = 10091

Now multiplying the highest exponent prime factors to calculate the LCM of 1008 and 1009.

LCM(1008,1009) = 24×32×71×10091
LCM(1008,1009) = 1017072

Factors of 1008

List of positive integer factors of 1008 that divides 1008 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008

Factors of 1009

List of positive integer factors of 1009 that divides 1009 without a remainder.

1, 1009

Least Common Multiple of 1008 and 1009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1008 and 1009, than apply into the LCM equation.

GCF(1008,1009) = 1
LCM(1008,1009) = ( 1008 × 1009) / 1
LCM(1008,1009) = 1017072 / 1
LCM(1008,1009) = 1017072

Properties of LCM 1008 and 1009

(i) The LCM of 1009 and 1008 is associative

LCM of 1008 and 1009 = LCM of 1009 and 1008

Related Least Common Multiples of 1008

Related Least Common Multiples of 1009

Frequently Asked Questions on LCM of 1008 and 1009

1. What is the LCM of 1008 and 1009?

Answer: LCM of 1008 and 1009 is 1017072.

2. What are the Factors of 1008?

Answer: Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. There are 30 integers that are factors of 1008. The greatest factor of 1008 is 1008.

3. What are the Factors of 1009?

Answer: Factors of 1009 are 1, 1009. There are 2 integers that are factors of 1009. The greatest factor of 1009 is 1009.

4. How to Find the LCM of 1008 and 1009?

Answer:

Least Common Multiple of 1008 and 1009 = 1017072

Step 1: Find the prime factorization of 1008

1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 1009

1009 = 1009

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

LCM = 1017072 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 1009

Step 4: Therefore, the least common multiple of 1008 and 1009 is 1017072.