Least Common Multiple of 1008 and 1013

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 1013 the smallest integer that is 1021104 that is divisible by both numbers.

Least Common Multiple (LCM) of 1008 and 1013 is 1021104.

LCM(1008,1013) = 1021104

LCM of 1008 and 1013

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

LCM of:
and

Least Common Multiple of 1008 and 1013

LCM of 1008 and 1013 is 1021104

Least common multiple can be found by multiplying the highest exponent prime factors of 1008 and 1013. First we will calculate the prime factors of 1008 and 1013.

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 1013


1013 1013
1

Prime factors of 1013 are 1013. Prime factorization of 1013 in exponential form is:

1013 = 10131

Now multiplying the highest exponent prime factors to calculate the LCM of 1008 and 1013.

LCM(1008,1013) = 24×32×71×10131
LCM(1008,1013) = 1021104

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 1013

List of positive integer factors of 1013 that divides 1013 without a remainder.

1, 1013

Least Common Multiple of 1008 and 1013 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 1013, than apply into the LCM equation.

GCF(1008,1013) = 1
LCM(1008,1013) = ( 1008 × 1013) / 1
LCM(1008,1013) = 1021104 / 1
LCM(1008,1013) = 1021104

Properties of LCM 1008 and 1013

(i) The LCM of 1013 and 1008 is associative

LCM of 1008 and 1013 = LCM of 1013 and 1008

Related Least Common Multiples of 1008

Related Least Common Multiples of 1013

Frequently Asked Questions on LCM of 1008 and 1013

1. What is the LCM of 1008 and 1013?

Answer: LCM of 1008 and 1013 is 1021104.

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 1013?

Answer: Factors of 1013 are 1, 1013. There are 2 integers that are factors of 1013. The greatest factor of 1013 is 1013.

4. How to Find the LCM of 1008 and 1013?

Answer:

Least Common Multiple of 1008 and 1013 = 1021104

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 1013

1013 = 1013

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

LCM = 1021104 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 1013

Step 4: Therefore, the least common multiple of 1008 and 1013 is 1021104.