Least Common Multiple of 1014 and 1020

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1014 and 1020 the smallest integer that is 172380 that is divisible by both numbers.

Least Common Multiple (LCM) of 1014 and 1020 is 172380.

LCM(1014,1020) = 172380

LCM of 1014 and 1020

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

LCM of:
and

Least Common Multiple of 1014 and 1020

LCM of 1014 and 1020 is 172380

Least common multiple can be found by multiplying the highest exponent prime factors of 1014 and 1020. First we will calculate the prime factors of 1014 and 1020.

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

Prime Factorization of 1020


2 1020
2 510
3 255
5 85
17 17
1

Prime factors of 1020 are 2, 3, 5,17. Prime factorization of 1020 in exponential form is:

1020 = 22×31×51×171

Now multiplying the highest exponent prime factors to calculate the LCM of 1014 and 1020.

LCM(1014,1020) = 22×31×51×132×171
LCM(1014,1020) = 172380

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

Factors of 1020

List of positive integer factors of 1020 that divides 1020 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510, 1020

Least Common Multiple of 1014 and 1020 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1014 and 1020, than apply into the LCM equation.

GCF(1014,1020) = 6
LCM(1014,1020) = ( 1014 × 1020) / 6
LCM(1014,1020) = 1034280 / 6
LCM(1014,1020) = 172380

Properties of LCM 1014 and 1020

(i) The LCM of 1020 and 1014 is associative

LCM of 1014 and 1020 = LCM of 1020 and 1014

Related Least Common Multiples of 1014

Related Least Common Multiples of 1020

Frequently Asked Questions on LCM of 1014 and 1020

1. What is the LCM of 1014 and 1020?

Answer: LCM of 1014 and 1020 is 172380.

2. 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.

3. What are the Factors of 1020?

Answer: Factors of 1020 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510, 1020. There are 24 integers that are factors of 1020. The greatest factor of 1020 is 1020.

4. How to Find the LCM of 1014 and 1020?

Answer:

Least Common Multiple of 1014 and 1020 = 172380

Step 1: Find the prime factorization of 1014

1014 = 2 x 3 x 13 x 13

Step 2: Find the prime factorization of 1020

1020 = 2 x 2 x 3 x 5 x 17

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

LCM = 172380 = 2 x 2 x 3 x 5 x 13 x 13 x 17

Step 4: Therefore, the least common multiple of 1014 and 1020 is 172380.