Least Common Multiple of 1440 and 1442

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 1442 the smallest integer that is 1038240 that is divisible by both numbers.

Least Common Multiple (LCM) of 1440 and 1442 is 1038240.

LCM(1440,1442) = 1038240

LCM of 1440 and 1442

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

LCM of:
and

Least Common Multiple of 1440 and 1442

LCM of 1440 and 1442 is 1038240

Least common multiple can be found by multiplying the highest exponent prime factors of 1440 and 1442. First we will calculate the prime factors of 1440 and 1442.

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 1442


2 1442
7 721
103 103
1

Prime factors of 1442 are 2, 7,103. Prime factorization of 1442 in exponential form is:

1442 = 21×71×1031

Now multiplying the highest exponent prime factors to calculate the LCM of 1440 and 1442.

LCM(1440,1442) = 25×32×51×71×1031
LCM(1440,1442) = 1038240

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 1442

List of positive integer factors of 1442 that divides 1442 without a remainder.

1, 2, 7, 14, 103, 206, 721, 1442

Least Common Multiple of 1440 and 1442 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 1442, than apply into the LCM equation.

GCF(1440,1442) = 2
LCM(1440,1442) = ( 1440 × 1442) / 2
LCM(1440,1442) = 2076480 / 2
LCM(1440,1442) = 1038240

Properties of LCM 1440 and 1442

(i) The LCM of 1442 and 1440 is associative

LCM of 1440 and 1442 = LCM of 1442 and 1440

Related Least Common Multiples of 1440

Related Least Common Multiples of 1442

Frequently Asked Questions on LCM of 1440 and 1442

1. What is the LCM of 1440 and 1442?

Answer: LCM of 1440 and 1442 is 1038240.

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 1442?

Answer: Factors of 1442 are 1, 2, 7, 14, 103, 206, 721, 1442. There are 8 integers that are factors of 1442. The greatest factor of 1442 is 1442.

4. How to Find the LCM of 1440 and 1442?

Answer:

Least Common Multiple of 1440 and 1442 = 1038240

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 1442

1442 = 2 x 7 x 103

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

LCM = 1038240 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 103

Step 4: Therefore, the least common multiple of 1440 and 1442 is 1038240.