Least Common Multiple of 1449 and 1456

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1449 and 1456 the smallest integer that is 301392 that is divisible by both numbers.

Least Common Multiple (LCM) of 1449 and 1456 is 301392.

LCM(1449,1456) = 301392

LCM of 1449 and 1456

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

LCM of:
and

Least Common Multiple of 1449 and 1456

LCM of 1449 and 1456 is 301392

Least common multiple can be found by multiplying the highest exponent prime factors of 1449 and 1456. First we will calculate the prime factors of 1449 and 1456.

Prime Factorization of 1449


3 1449
3 483
7 161
23 23
1

Prime factors of 1449 are 3, 7,23. Prime factorization of 1449 in exponential form is:

1449 = 32×71×231

Prime Factorization of 1456


2 1456
2 728
2 364
2 182
7 91
13 13
1

Prime factors of 1456 are 2, 7,13. Prime factorization of 1456 in exponential form is:

1456 = 24×71×131

Now multiplying the highest exponent prime factors to calculate the LCM of 1449 and 1456.

LCM(1449,1456) = 24×32×71×131×231
LCM(1449,1456) = 301392

Factors of 1449

List of positive integer factors of 1449 that divides 1449 without a remainder.

1, 3, 7, 9, 21, 23, 63, 69, 161, 207, 483, 1449

Factors of 1456

List of positive integer factors of 1456 that divides 1456 without a remainder.

1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 52, 56, 91, 104, 112, 182, 208, 364, 728, 1456

Least Common Multiple of 1449 and 1456 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1449 and 1456, than apply into the LCM equation.

GCF(1449,1456) = 7
LCM(1449,1456) = ( 1449 × 1456) / 7
LCM(1449,1456) = 2109744 / 7
LCM(1449,1456) = 301392

Properties of LCM 1449 and 1456

(i) The LCM of 1456 and 1449 is associative

LCM of 1449 and 1456 = LCM of 1456 and 1449

Related Least Common Multiples of 1449

Related Least Common Multiples of 1456

Frequently Asked Questions on LCM of 1449 and 1456

1. What is the LCM of 1449 and 1456?

Answer: LCM of 1449 and 1456 is 301392.

2. What are the Factors of 1449?

Answer: Factors of 1449 are 1, 3, 7, 9, 21, 23, 63, 69, 161, 207, 483, 1449. There are 12 integers that are factors of 1449. The greatest factor of 1449 is 1449.

3. What are the Factors of 1456?

Answer: Factors of 1456 are 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 52, 56, 91, 104, 112, 182, 208, 364, 728, 1456. There are 20 integers that are factors of 1456. The greatest factor of 1456 is 1456.

4. How to Find the LCM of 1449 and 1456?

Answer:

Least Common Multiple of 1449 and 1456 = 301392

Step 1: Find the prime factorization of 1449

1449 = 3 x 3 x 7 x 23

Step 2: Find the prime factorization of 1456

1456 = 2 x 2 x 2 x 2 x 7 x 13

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

LCM = 301392 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 13 x 23

Step 4: Therefore, the least common multiple of 1449 and 1456 is 301392.