Least Common Multiple of 1002 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 1002 and 1008 the smallest integer that is 168336 that is divisible by both numbers.

Least Common Multiple (LCM) of 1002 and 1008 is 168336.

LCM(1002,1008) = 168336

LCM of 1002 and 1008

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

LCM of:
and

Least Common Multiple of 1002 and 1008

LCM of 1002 and 1008 is 168336

Least common multiple can be found by multiplying the highest exponent prime factors of 1002 and 1008. First we will calculate the prime factors of 1002 and 1008.

Prime Factorization of 1002


2 1002
3 501
167 167
1

Prime factors of 1002 are 2, 3,167. Prime factorization of 1002 in exponential form is:

1002 = 21×31×1671

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 1002 and 1008.

LCM(1002,1008) = 24×32×71×1671
LCM(1002,1008) = 168336

Factors of 1002

List of positive integer factors of 1002 that divides 1002 without a remainder.

1, 2, 3, 6, 167, 334, 501, 1002

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 1002 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 1002 and 1008, than apply into the LCM equation.

GCF(1002,1008) = 6
LCM(1002,1008) = ( 1002 × 1008) / 6
LCM(1002,1008) = 1010016 / 6
LCM(1002,1008) = 168336

Properties of LCM 1002 and 1008

(i) The LCM of 1008 and 1002 is associative

LCM of 1002 and 1008 = LCM of 1008 and 1002

Related Least Common Multiples of 1002

Related Least Common Multiples of 1008

Frequently Asked Questions on LCM of 1002 and 1008

1. What is the LCM of 1002 and 1008?

Answer: LCM of 1002 and 1008 is 168336.

2. What are the Factors of 1002?

Answer: Factors of 1002 are 1, 2, 3, 6, 167, 334, 501, 1002. There are 8 integers that are factors of 1002. The greatest factor of 1002 is 1002.

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 1002 and 1008?

Answer:

Least Common Multiple of 1002 and 1008 = 168336

Step 1: Find the prime factorization of 1002

1002 = 2 x 3 x 167

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 = 168336 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 167

Step 4: Therefore, the least common multiple of 1002 and 1008 is 168336.