Least Common Multiple of 1012 and 1014

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1012 and 1014 the smallest integer that is 513084 that is divisible by both numbers.

Least Common Multiple (LCM) of 1012 and 1014 is 513084.

LCM(1012,1014) = 513084

LCM of 1012 and 1014

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

LCM of:
and

Least Common Multiple of 1012 and 1014

LCM of 1012 and 1014 is 513084

Least common multiple can be found by multiplying the highest exponent prime factors of 1012 and 1014. First we will calculate the prime factors of 1012 and 1014.

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

Prime Factorization of 1014


2 1014
3 507
13 169
13 13
1

Prime factors of 1014 are 2, 3,13. Prime factorization of 1014 in exponential form is:

1014 = 21×31×132

Now multiplying the highest exponent prime factors to calculate the LCM of 1012 and 1014.

LCM(1012,1014) = 22×31×111×132×231
LCM(1012,1014) = 513084

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

Factors of 1014

List of positive integer factors of 1014 that divides 1014 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014

Least Common Multiple of 1012 and 1014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1012 and 1014, than apply into the LCM equation.

GCF(1012,1014) = 2
LCM(1012,1014) = ( 1012 × 1014) / 2
LCM(1012,1014) = 1026168 / 2
LCM(1012,1014) = 513084

Properties of LCM 1012 and 1014

(i) The LCM of 1014 and 1012 is associative

LCM of 1012 and 1014 = LCM of 1014 and 1012

Related Least Common Multiples of 1012

Related Least Common Multiples of 1014

Frequently Asked Questions on LCM of 1012 and 1014

1. What is the LCM of 1012 and 1014?

Answer: LCM of 1012 and 1014 is 513084.

2. 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.

3. What are the Factors of 1014?

Answer: Factors of 1014 are 1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014. There are 12 integers that are factors of 1014. The greatest factor of 1014 is 1014.

4. How to Find the LCM of 1012 and 1014?

Answer:

Least Common Multiple of 1012 and 1014 = 513084

Step 1: Find the prime factorization of 1012

1012 = 2 x 2 x 11 x 23

Step 2: Find the prime factorization of 1014

1014 = 2 x 3 x 13 x 13

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

LCM = 513084 = 2 x 2 x 3 x 11 x 13 x 13 x 23

Step 4: Therefore, the least common multiple of 1012 and 1014 is 513084.