Least Common Multiple of 1008 and 1010

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 1010 the smallest integer that is 509040 that is divisible by both numbers.

Least Common Multiple (LCM) of 1008 and 1010 is 509040.

LCM(1008,1010) = 509040

LCM of 1008 and 1010

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

LCM of:
and

Least Common Multiple of 1008 and 1010

LCM of 1008 and 1010 is 509040

Least common multiple can be found by multiplying the highest exponent prime factors of 1008 and 1010. First we will calculate the prime factors of 1008 and 1010.

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 1010


2 1010
5 505
101 101
1

Prime factors of 1010 are 2, 5,101. Prime factorization of 1010 in exponential form is:

1010 = 21×51×1011

Now multiplying the highest exponent prime factors to calculate the LCM of 1008 and 1010.

LCM(1008,1010) = 24×32×51×71×1011
LCM(1008,1010) = 509040

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 1010

List of positive integer factors of 1010 that divides 1010 without a remainder.

1, 2, 5, 10, 101, 202, 505, 1010

Least Common Multiple of 1008 and 1010 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 1010, than apply into the LCM equation.

GCF(1008,1010) = 2
LCM(1008,1010) = ( 1008 × 1010) / 2
LCM(1008,1010) = 1018080 / 2
LCM(1008,1010) = 509040

Properties of LCM 1008 and 1010

(i) The LCM of 1010 and 1008 is associative

LCM of 1008 and 1010 = LCM of 1010 and 1008

Related Least Common Multiples of 1008

Related Least Common Multiples of 1010

Frequently Asked Questions on LCM of 1008 and 1010

1. What is the LCM of 1008 and 1010?

Answer: LCM of 1008 and 1010 is 509040.

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 1010?

Answer: Factors of 1010 are 1, 2, 5, 10, 101, 202, 505, 1010. There are 8 integers that are factors of 1010. The greatest factor of 1010 is 1010.

4. How to Find the LCM of 1008 and 1010?

Answer:

Least Common Multiple of 1008 and 1010 = 509040

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 1010

1010 = 2 x 5 x 101

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

LCM = 509040 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 101

Step 4: Therefore, the least common multiple of 1008 and 1010 is 509040.