Least Common Multiple of 2016 and 2023

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2016 and 2023 the smallest integer that is 582624 that is divisible by both numbers.

Least Common Multiple (LCM) of 2016 and 2023 is 582624.

LCM(2016,2023) = 582624

LCM of 2016 and 2023

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

LCM of:
and

Least Common Multiple of 2016 and 2023

LCM of 2016 and 2023 is 582624

Least common multiple can be found by multiplying the highest exponent prime factors of 2016 and 2023. First we will calculate the prime factors of 2016 and 2023.

Prime Factorization of 2016


2 2016
2 1008
2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 2016 are 2, 3,7. Prime factorization of 2016 in exponential form is:

2016 = 25×32×71

Prime Factorization of 2023


7 2023
17 289
17 17
1

Prime factors of 2023 are 7,17. Prime factorization of 2023 in exponential form is:

2023 = 71×172

Now multiplying the highest exponent prime factors to calculate the LCM of 2016 and 2023.

LCM(2016,2023) = 25×32×71×172
LCM(2016,2023) = 582624

Factors of 2016

List of positive integer factors of 2016 that divides 2016 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016

Factors of 2023

List of positive integer factors of 2023 that divides 2023 without a remainder.

1, 7, 17, 119, 289, 2023

Least Common Multiple of 2016 and 2023 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2016 and 2023, than apply into the LCM equation.

GCF(2016,2023) = 7
LCM(2016,2023) = ( 2016 × 2023) / 7
LCM(2016,2023) = 4078368 / 7
LCM(2016,2023) = 582624

Properties of LCM 2016 and 2023

(i) The LCM of 2023 and 2016 is associative

LCM of 2016 and 2023 = LCM of 2023 and 2016

Related Least Common Multiples of 2016

Related Least Common Multiples of 2023

Frequently Asked Questions on LCM of 2016 and 2023

1. What is the LCM of 2016 and 2023?

Answer: LCM of 2016 and 2023 is 582624.

2. What are the Factors of 2016?

Answer: Factors of 2016 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016. There are 36 integers that are factors of 2016. The greatest factor of 2016 is 2016.

3. What are the Factors of 2023?

Answer: Factors of 2023 are 1, 7, 17, 119, 289, 2023. There are 6 integers that are factors of 2023. The greatest factor of 2023 is 2023.

4. How to Find the LCM of 2016 and 2023?

Answer:

Least Common Multiple of 2016 and 2023 = 582624

Step 1: Find the prime factorization of 2016

2016 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7

Step 2: Find the prime factorization of 2023

2023 = 7 x 17 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 = 582624 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 17 x 17

Step 4: Therefore, the least common multiple of 2016 and 2023 is 582624.