Least Common Multiple of 2040 and 2048

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2040 and 2048 the smallest integer that is 522240 that is divisible by both numbers.

Least Common Multiple (LCM) of 2040 and 2048 is 522240.

LCM(2040,2048) = 522240

LCM of 2040 and 2048

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

LCM of:
and

Least Common Multiple of 2040 and 2048

LCM of 2040 and 2048 is 522240

Least common multiple can be found by multiplying the highest exponent prime factors of 2040 and 2048. First we will calculate the prime factors of 2040 and 2048.

Prime Factorization of 2040


2 2040
2 1020
2 510
3 255
5 85
17 17
1

Prime factors of 2040 are 2, 3, 5,17. Prime factorization of 2040 in exponential form is:

2040 = 23×31×51×171

Prime Factorization of 2048


2 2048
2 1024
2 512
2 256
2 128
2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 2048 are 2. Prime factorization of 2048 in exponential form is:

2048 = 211

Now multiplying the highest exponent prime factors to calculate the LCM of 2040 and 2048.

LCM(2040,2048) = 211×31×51×171
LCM(2040,2048) = 522240

Factors of 2040

List of positive integer factors of 2040 that divides 2040 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, 2040

Factors of 2048

List of positive integer factors of 2048 that divides 2048 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048

Least Common Multiple of 2040 and 2048 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2040 and 2048, than apply into the LCM equation.

GCF(2040,2048) = 8
LCM(2040,2048) = ( 2040 × 2048) / 8
LCM(2040,2048) = 4177920 / 8
LCM(2040,2048) = 522240

Properties of LCM 2040 and 2048

(i) The LCM of 2048 and 2040 is associative

LCM of 2040 and 2048 = LCM of 2048 and 2040

Related Least Common Multiples of 2040

Related Least Common Multiples of 2048

Frequently Asked Questions on LCM of 2040 and 2048

1. What is the LCM of 2040 and 2048?

Answer: LCM of 2040 and 2048 is 522240.

2. What are the Factors of 2040?

Answer: Factors of 2040 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 340, 408, 510, 680, 1020, 2040. There are 32 integers that are factors of 2040. The greatest factor of 2040 is 2040.

3. What are the Factors of 2048?

Answer: Factors of 2048 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048. There are 12 integers that are factors of 2048. The greatest factor of 2048 is 2048.

4. How to Find the LCM of 2040 and 2048?

Answer:

Least Common Multiple of 2040 and 2048 = 522240

Step 1: Find the prime factorization of 2040

2040 = 2 x 2 x 2 x 3 x 5 x 17

Step 2: Find the prime factorization of 2048

2048 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

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

LCM = 522240 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 2040 and 2048 is 522240.