Least Common Multiple of 1440 and 1441

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1440 and 1441 the smallest integer that is 2075040 that is divisible by both numbers.

Least Common Multiple (LCM) of 1440 and 1441 is 2075040.

LCM(1440,1441) = 2075040

LCM of 1440 and 1441

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

LCM of:
and

Least Common Multiple of 1440 and 1441

LCM of 1440 and 1441 is 2075040

Least common multiple can be found by multiplying the highest exponent prime factors of 1440 and 1441. First we will calculate the prime factors of 1440 and 1441.

Prime Factorization of 1440


2 1440
2 720
2 360
2 180
2 90
3 45
3 15
5 5
1

Prime factors of 1440 are 2, 3,5. Prime factorization of 1440 in exponential form is:

1440 = 25×32×51

Prime Factorization of 1441


11 1441
131 131
1

Prime factors of 1441 are 11,131. Prime factorization of 1441 in exponential form is:

1441 = 111×1311

Now multiplying the highest exponent prime factors to calculate the LCM of 1440 and 1441.

LCM(1440,1441) = 25×32×51×111×1311
LCM(1440,1441) = 2075040

Factors of 1440

List of positive integer factors of 1440 that divides 1440 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720, 1440

Factors of 1441

List of positive integer factors of 1441 that divides 1441 without a remainder.

1, 11, 131, 1441

Least Common Multiple of 1440 and 1441 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1440 and 1441, than apply into the LCM equation.

GCF(1440,1441) = 1
LCM(1440,1441) = ( 1440 × 1441) / 1
LCM(1440,1441) = 2075040 / 1
LCM(1440,1441) = 2075040

Properties of LCM 1440 and 1441

(i) The LCM of 1441 and 1440 is associative

LCM of 1440 and 1441 = LCM of 1441 and 1440

Related Least Common Multiples of 1440

Related Least Common Multiples of 1441

Frequently Asked Questions on LCM of 1440 and 1441

1. What is the LCM of 1440 and 1441?

Answer: LCM of 1440 and 1441 is 2075040.

2. What are the Factors of 1440?

Answer: Factors of 1440 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720, 1440. There are 36 integers that are factors of 1440. The greatest factor of 1440 is 1440.

3. What are the Factors of 1441?

Answer: Factors of 1441 are 1, 11, 131, 1441. There are 4 integers that are factors of 1441. The greatest factor of 1441 is 1441.

4. How to Find the LCM of 1440 and 1441?

Answer:

Least Common Multiple of 1440 and 1441 = 2075040

Step 1: Find the prime factorization of 1440

1440 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5

Step 2: Find the prime factorization of 1441

1441 = 11 x 131

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

LCM = 2075040 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11 x 131

Step 4: Therefore, the least common multiple of 1440 and 1441 is 2075040.