Least Common Multiple of 1005 and 1012

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1005 and 1012 the smallest integer that is 1017060 that is divisible by both numbers.

Least Common Multiple (LCM) of 1005 and 1012 is 1017060.

LCM(1005,1012) = 1017060

LCM of 1005 and 1012

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

LCM of:
and

Least Common Multiple of 1005 and 1012

LCM of 1005 and 1012 is 1017060

Least common multiple can be found by multiplying the highest exponent prime factors of 1005 and 1012. First we will calculate the prime factors of 1005 and 1012.

Prime Factorization of 1005


3 1005
5 335
67 67
1

Prime factors of 1005 are 3, 5,67. Prime factorization of 1005 in exponential form is:

1005 = 31×51×671

Prime Factorization of 1012


2 1012
2 506
11 253
23 23
1

Prime factors of 1012 are 2, 11,23. Prime factorization of 1012 in exponential form is:

1012 = 22×111×231

Now multiplying the highest exponent prime factors to calculate the LCM of 1005 and 1012.

LCM(1005,1012) = 22×31×51×111×231×671
LCM(1005,1012) = 1017060

Factors of 1005

List of positive integer factors of 1005 that divides 1005 without a remainder.

1, 3, 5, 15, 67, 201, 335, 1005

Factors of 1012

List of positive integer factors of 1012 that divides 1012 without a remainder.

1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012

Least Common Multiple of 1005 and 1012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1005 and 1012, than apply into the LCM equation.

GCF(1005,1012) = 1
LCM(1005,1012) = ( 1005 × 1012) / 1
LCM(1005,1012) = 1017060 / 1
LCM(1005,1012) = 1017060

Properties of LCM 1005 and 1012

(i) The LCM of 1012 and 1005 is associative

LCM of 1005 and 1012 = LCM of 1012 and 1005

Related Least Common Multiples of 1005

Related Least Common Multiples of 1012

Frequently Asked Questions on LCM of 1005 and 1012

1. What is the LCM of 1005 and 1012?

Answer: LCM of 1005 and 1012 is 1017060.

2. What are the Factors of 1005?

Answer: Factors of 1005 are 1, 3, 5, 15, 67, 201, 335, 1005. There are 8 integers that are factors of 1005. The greatest factor of 1005 is 1005.

3. What are the Factors of 1012?

Answer: Factors of 1012 are 1, 2, 4, 11, 22, 23, 44, 46, 92, 253, 506, 1012. There are 12 integers that are factors of 1012. The greatest factor of 1012 is 1012.

4. How to Find the LCM of 1005 and 1012?

Answer:

Least Common Multiple of 1005 and 1012 = 1017060

Step 1: Find the prime factorization of 1005

1005 = 3 x 5 x 67

Step 2: Find the prime factorization of 1012

1012 = 2 x 2 x 11 x 23

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

LCM = 1017060 = 2 x 2 x 3 x 5 x 11 x 23 x 67

Step 4: Therefore, the least common multiple of 1005 and 1012 is 1017060.