Least Common Multiple of 2040 and 2046

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 2046 the smallest integer that is 695640 that is divisible by both numbers.

Least Common Multiple (LCM) of 2040 and 2046 is 695640.

LCM(2040,2046) = 695640

LCM of 2040 and 2046

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

LCM of:
and

Least Common Multiple of 2040 and 2046

LCM of 2040 and 2046 is 695640

Least common multiple can be found by multiplying the highest exponent prime factors of 2040 and 2046. First we will calculate the prime factors of 2040 and 2046.

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 2046


2 2046
3 1023
11 341
31 31
1

Prime factors of 2046 are 2, 3, 11,31. Prime factorization of 2046 in exponential form is:

2046 = 21×31×111×311

Now multiplying the highest exponent prime factors to calculate the LCM of 2040 and 2046.

LCM(2040,2046) = 23×31×51×111×171×311
LCM(2040,2046) = 695640

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 2046

List of positive integer factors of 2046 that divides 2046 without a remainder.

1, 2, 3, 6, 11, 22, 31, 33, 62, 66, 93, 186, 341, 682, 1023, 2046

Least Common Multiple of 2040 and 2046 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 2046, than apply into the LCM equation.

GCF(2040,2046) = 6
LCM(2040,2046) = ( 2040 × 2046) / 6
LCM(2040,2046) = 4173840 / 6
LCM(2040,2046) = 695640

Properties of LCM 2040 and 2046

(i) The LCM of 2046 and 2040 is associative

LCM of 2040 and 2046 = LCM of 2046 and 2040

Related Least Common Multiples of 2040

Related Least Common Multiples of 2046

Frequently Asked Questions on LCM of 2040 and 2046

1. What is the LCM of 2040 and 2046?

Answer: LCM of 2040 and 2046 is 695640.

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 2046?

Answer: Factors of 2046 are 1, 2, 3, 6, 11, 22, 31, 33, 62, 66, 93, 186, 341, 682, 1023, 2046. There are 16 integers that are factors of 2046. The greatest factor of 2046 is 2046.

4. How to Find the LCM of 2040 and 2046?

Answer:

Least Common Multiple of 2040 and 2046 = 695640

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 2046

2046 = 2 x 3 x 11 x 31

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

LCM = 695640 = 2 x 2 x 2 x 3 x 5 x 11 x 17 x 31

Step 4: Therefore, the least common multiple of 2040 and 2046 is 695640.