Least Common Multiple of 2009 and 2017

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2009 and 2017 the smallest integer that is 4052153 that is divisible by both numbers.

Least Common Multiple (LCM) of 2009 and 2017 is 4052153.

LCM(2009,2017) = 4052153

LCM of 2009 and 2017

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

LCM of:
and

Least Common Multiple of 2009 and 2017

LCM of 2009 and 2017 is 4052153

Least common multiple can be found by multiplying the highest exponent prime factors of 2009 and 2017. First we will calculate the prime factors of 2009 and 2017.

Prime Factorization of 2009


7 2009
7 287
41 41
1

Prime factors of 2009 are 7,41. Prime factorization of 2009 in exponential form is:

2009 = 72×411

Prime Factorization of 2017


2017 2017
1

Prime factors of 2017 are 2017. Prime factorization of 2017 in exponential form is:

2017 = 20171

Now multiplying the highest exponent prime factors to calculate the LCM of 2009 and 2017.

LCM(2009,2017) = 72×411×20171
LCM(2009,2017) = 4052153

Factors of 2009

List of positive integer factors of 2009 that divides 2009 without a remainder.

1, 7, 41, 49, 287, 2009

Factors of 2017

List of positive integer factors of 2017 that divides 2017 without a remainder.

1, 2017

Least Common Multiple of 2009 and 2017 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2009 and 2017, than apply into the LCM equation.

GCF(2009,2017) = 1
LCM(2009,2017) = ( 2009 × 2017) / 1
LCM(2009,2017) = 4052153 / 1
LCM(2009,2017) = 4052153

Properties of LCM 2009 and 2017

(i) The LCM of 2017 and 2009 is associative

LCM of 2009 and 2017 = LCM of 2017 and 2009

Related Least Common Multiples of 2009

Related Least Common Multiples of 2017

Frequently Asked Questions on LCM of 2009 and 2017

1. What is the LCM of 2009 and 2017?

Answer: LCM of 2009 and 2017 is 4052153.

2. What are the Factors of 2009?

Answer: Factors of 2009 are 1, 7, 41, 49, 287, 2009. There are 6 integers that are factors of 2009. The greatest factor of 2009 is 2009.

3. What are the Factors of 2017?

Answer: Factors of 2017 are 1, 2017. There are 2 integers that are factors of 2017. The greatest factor of 2017 is 2017.

4. How to Find the LCM of 2009 and 2017?

Answer:

Least Common Multiple of 2009 and 2017 = 4052153

Step 1: Find the prime factorization of 2009

2009 = 7 x 7 x 41

Step 2: Find the prime factorization of 2017

2017 = 2017

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

LCM = 4052153 = 7 x 7 x 41 x 2017

Step 4: Therefore, the least common multiple of 2009 and 2017 is 4052153.