Least Common Multiple of 1000 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 1000 and 1008 the smallest integer that is 126000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1000 and 1008 is 126000.

LCM(1000,1008) = 126000

LCM of 1000 and 1008

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

LCM of:
and

Least Common Multiple of 1000 and 1008

LCM of 1000 and 1008 is 126000

Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1008. First we will calculate the prime factors of 1000 and 1008.

Prime Factorization of 1000


2 1000
2 500
2 250
5 125
5 25
5 5
1

Prime factors of 1000 are 2,5. Prime factorization of 1000 in exponential form is:

1000 = 23×53

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 1000 and 1008.

LCM(1000,1008) = 24×32×53×71
LCM(1000,1008) = 126000

Factors of 1000

List of positive integer factors of 1000 that divides 1000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

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 1000 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 1000 and 1008, than apply into the LCM equation.

GCF(1000,1008) = 8
LCM(1000,1008) = ( 1000 × 1008) / 8
LCM(1000,1008) = 1008000 / 8
LCM(1000,1008) = 126000

Properties of LCM 1000 and 1008

(i) The LCM of 1008 and 1000 is associative

LCM of 1000 and 1008 = LCM of 1008 and 1000

Related Least Common Multiples of 1000

Related Least Common Multiples of 1008

Frequently Asked Questions on LCM of 1000 and 1008

1. What is the LCM of 1000 and 1008?

Answer: LCM of 1000 and 1008 is 126000.

2. What are the Factors of 1000?

Answer: Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000. There are 16 integers that are factors of 1000. The greatest factor of 1000 is 1000.

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 1000 and 1008?

Answer:

Least Common Multiple of 1000 and 1008 = 126000

Step 1: Find the prime factorization of 1000

1000 = 2 x 2 x 2 x 5 x 5 x 5

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 = 126000 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 1000 and 1008 is 126000.