Least Common Multiple of 1440 and 1448

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 1448 the smallest integer that is 260640 that is divisible by both numbers.

Least Common Multiple (LCM) of 1440 and 1448 is 260640.

LCM(1440,1448) = 260640

LCM of 1440 and 1448

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

LCM of:
and

Least Common Multiple of 1440 and 1448

LCM of 1440 and 1448 is 260640

Least common multiple can be found by multiplying the highest exponent prime factors of 1440 and 1448. First we will calculate the prime factors of 1440 and 1448.

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 1448


2 1448
2 724
2 362
181 181
1

Prime factors of 1448 are 2,181. Prime factorization of 1448 in exponential form is:

1448 = 23×1811

Now multiplying the highest exponent prime factors to calculate the LCM of 1440 and 1448.

LCM(1440,1448) = 25×32×51×1811
LCM(1440,1448) = 260640

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 1448

List of positive integer factors of 1448 that divides 1448 without a remainder.

1, 2, 4, 8, 181, 362, 724, 1448

Least Common Multiple of 1440 and 1448 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 1448, than apply into the LCM equation.

GCF(1440,1448) = 8
LCM(1440,1448) = ( 1440 × 1448) / 8
LCM(1440,1448) = 2085120 / 8
LCM(1440,1448) = 260640

Properties of LCM 1440 and 1448

(i) The LCM of 1448 and 1440 is associative

LCM of 1440 and 1448 = LCM of 1448 and 1440

Related Least Common Multiples of 1440

Related Least Common Multiples of 1448

Frequently Asked Questions on LCM of 1440 and 1448

1. What is the LCM of 1440 and 1448?

Answer: LCM of 1440 and 1448 is 260640.

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 1448?

Answer: Factors of 1448 are 1, 2, 4, 8, 181, 362, 724, 1448. There are 8 integers that are factors of 1448. The greatest factor of 1448 is 1448.

4. How to Find the LCM of 1440 and 1448?

Answer:

Least Common Multiple of 1440 and 1448 = 260640

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 1448

1448 = 2 x 2 x 2 x 181

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

LCM = 260640 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 181

Step 4: Therefore, the least common multiple of 1440 and 1448 is 260640.