Least Common Multiple of 1007 and 1008

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1007 and 1008 the smallest integer that is 1015056 that is divisible by both numbers.

Least Common Multiple (LCM) of 1007 and 1008 is 1015056.

LCM(1007,1008) = 1015056

LCM of 1007 and 1008

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

LCM of:
and

Least Common Multiple of 1007 and 1008

LCM of 1007 and 1008 is 1015056

Least common multiple can be found by multiplying the highest exponent prime factors of 1007 and 1008. First we will calculate the prime factors of 1007 and 1008.

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

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1007 and 1008.

LCM(1007,1008) = 24×32×71×191×531
LCM(1007,1008) = 1015056

Factors of 1007

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

1, 19, 53, 1007

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

Least Common Multiple of 1007 and 1008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1007 and 1008, than apply into the LCM equation.

GCF(1007,1008) = 1
LCM(1007,1008) = ( 1007 × 1008) / 1
LCM(1007,1008) = 1015056 / 1
LCM(1007,1008) = 1015056

Properties of LCM 1007 and 1008

(i) The LCM of 1008 and 1007 is associative

LCM of 1007 and 1008 = LCM of 1008 and 1007

Related Least Common Multiples of 1007

Related Least Common Multiples of 1008

Frequently Asked Questions on LCM of 1007 and 1008

1. What is the LCM of 1007 and 1008?

Answer: LCM of 1007 and 1008 is 1015056.

2. 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.

3. 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.

4. How to Find the LCM of 1007 and 1008?

Answer:

Least Common Multiple of 1007 and 1008 = 1015056

Step 1: Find the prime factorization of 1007

1007 = 19 x 53

Step 2: Find the prime factorization of 1008

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

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

LCM = 1015056 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 19 x 53

Step 4: Therefore, the least common multiple of 1007 and 1008 is 1015056.