Least Common Multiple of 2034 and 2040

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2034 and 2040 the smallest integer that is 691560 that is divisible by both numbers.

Least Common Multiple (LCM) of 2034 and 2040 is 691560.

LCM(2034,2040) = 691560

LCM of 2034 and 2040

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

LCM of:
and

Least Common Multiple of 2034 and 2040

LCM of 2034 and 2040 is 691560

Least common multiple can be found by multiplying the highest exponent prime factors of 2034 and 2040. First we will calculate the prime factors of 2034 and 2040.

Prime Factorization of 2034


2 2034
3 1017
3 339
113 113
1

Prime factors of 2034 are 2, 3,113. Prime factorization of 2034 in exponential form is:

2034 = 21×32×1131

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

Now multiplying the highest exponent prime factors to calculate the LCM of 2034 and 2040.

LCM(2034,2040) = 23×32×51×171×1131
LCM(2034,2040) = 691560

Factors of 2034

List of positive integer factors of 2034 that divides 2034 without a remainder.

1, 2, 3, 6, 9, 18, 113, 226, 339, 678, 1017, 2034

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

Least Common Multiple of 2034 and 2040 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2034 and 2040, than apply into the LCM equation.

GCF(2034,2040) = 6
LCM(2034,2040) = ( 2034 × 2040) / 6
LCM(2034,2040) = 4149360 / 6
LCM(2034,2040) = 691560

Properties of LCM 2034 and 2040

(i) The LCM of 2040 and 2034 is associative

LCM of 2034 and 2040 = LCM of 2040 and 2034

Related Least Common Multiples of 2034

Related Least Common Multiples of 2040

Frequently Asked Questions on LCM of 2034 and 2040

1. What is the LCM of 2034 and 2040?

Answer: LCM of 2034 and 2040 is 691560.

2. What are the Factors of 2034?

Answer: Factors of 2034 are 1, 2, 3, 6, 9, 18, 113, 226, 339, 678, 1017, 2034. There are 12 integers that are factors of 2034. The greatest factor of 2034 is 2034.

3. 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.

4. How to Find the LCM of 2034 and 2040?

Answer:

Least Common Multiple of 2034 and 2040 = 691560

Step 1: Find the prime factorization of 2034

2034 = 2 x 3 x 3 x 113

Step 2: Find the prime factorization of 2040

2040 = 2 x 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 = 691560 = 2 x 2 x 2 x 3 x 3 x 5 x 17 x 113

Step 4: Therefore, the least common multiple of 2034 and 2040 is 691560.