Least Common Multiple of 1017 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 1017 and 1020 the smallest integer that is 345780 that is divisible by both numbers.

Least Common Multiple (LCM) of 1017 and 1020 is 345780.

LCM(1017,1020) = 345780

LCM of 1017 and 1020

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

LCM of:
and

Least Common Multiple of 1017 and 1020

LCM of 1017 and 1020 is 345780

Least common multiple can be found by multiplying the highest exponent prime factors of 1017 and 1020. First we will calculate the prime factors of 1017 and 1020.

Prime Factorization of 1017


3 1017
3 339
113 113
1

Prime factors of 1017 are 3,113. Prime factorization of 1017 in exponential form is:

1017 = 32×1131

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 1017 and 1020.

LCM(1017,1020) = 22×32×51×171×1131
LCM(1017,1020) = 345780

Factors of 1017

List of positive integer factors of 1017 that divides 1017 without a remainder.

1, 3, 9, 113, 339, 1017

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 1017 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 1017 and 1020, than apply into the LCM equation.

GCF(1017,1020) = 3
LCM(1017,1020) = ( 1017 × 1020) / 3
LCM(1017,1020) = 1037340 / 3
LCM(1017,1020) = 345780

Properties of LCM 1017 and 1020

(i) The LCM of 1020 and 1017 is associative

LCM of 1017 and 1020 = LCM of 1020 and 1017

Related Least Common Multiples of 1017

Related Least Common Multiples of 1020

Frequently Asked Questions on LCM of 1017 and 1020

1. What is the LCM of 1017 and 1020?

Answer: LCM of 1017 and 1020 is 345780.

2. What are the Factors of 1017?

Answer: Factors of 1017 are 1, 3, 9, 113, 339, 1017. There are 6 integers that are factors of 1017. The greatest factor of 1017 is 1017.

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 1017 and 1020?

Answer:

Least Common Multiple of 1017 and 1020 = 345780

Step 1: Find the prime factorization of 1017

1017 = 3 x 3 x 113

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 = 345780 = 2 x 2 x 3 x 3 x 5 x 17 x 113

Step 4: Therefore, the least common multiple of 1017 and 1020 is 345780.