Least Common Multiple of 1440 and 1445

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 1445 the smallest integer that is 416160 that is divisible by both numbers.

Least Common Multiple (LCM) of 1440 and 1445 is 416160.

LCM(1440,1445) = 416160

LCM of 1440 and 1445

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

LCM of:
and

Least Common Multiple of 1440 and 1445

LCM of 1440 and 1445 is 416160

Least common multiple can be found by multiplying the highest exponent prime factors of 1440 and 1445. First we will calculate the prime factors of 1440 and 1445.

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 1445


5 1445
17 289
17 17
1

Prime factors of 1445 are 5,17. Prime factorization of 1445 in exponential form is:

1445 = 51×172

Now multiplying the highest exponent prime factors to calculate the LCM of 1440 and 1445.

LCM(1440,1445) = 25×32×51×172
LCM(1440,1445) = 416160

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 1445

List of positive integer factors of 1445 that divides 1445 without a remainder.

1, 5, 17, 85, 289, 1445

Least Common Multiple of 1440 and 1445 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 1445, than apply into the LCM equation.

GCF(1440,1445) = 5
LCM(1440,1445) = ( 1440 × 1445) / 5
LCM(1440,1445) = 2080800 / 5
LCM(1440,1445) = 416160

Properties of LCM 1440 and 1445

(i) The LCM of 1445 and 1440 is associative

LCM of 1440 and 1445 = LCM of 1445 and 1440

Related Least Common Multiples of 1440

Related Least Common Multiples of 1445

Frequently Asked Questions on LCM of 1440 and 1445

1. What is the LCM of 1440 and 1445?

Answer: LCM of 1440 and 1445 is 416160.

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 1445?

Answer: Factors of 1445 are 1, 5, 17, 85, 289, 1445. There are 6 integers that are factors of 1445. The greatest factor of 1445 is 1445.

4. How to Find the LCM of 1440 and 1445?

Answer:

Least Common Multiple of 1440 and 1445 = 416160

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 1445

1445 = 5 x 17 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 = 416160 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 17 x 17

Step 4: Therefore, the least common multiple of 1440 and 1445 is 416160.