Least Common Multiple of 1456 and 1460

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1456 and 1460 the smallest integer that is 531440 that is divisible by both numbers.

Least Common Multiple (LCM) of 1456 and 1460 is 531440.

LCM(1456,1460) = 531440

LCM of 1456 and 1460

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

LCM of:
and

Least Common Multiple of 1456 and 1460

LCM of 1456 and 1460 is 531440

Least common multiple can be found by multiplying the highest exponent prime factors of 1456 and 1460. First we will calculate the prime factors of 1456 and 1460.

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

Prime Factorization of 1460


2 1460
2 730
5 365
73 73
1

Prime factors of 1460 are 2, 5,73. Prime factorization of 1460 in exponential form is:

1460 = 22×51×731

Now multiplying the highest exponent prime factors to calculate the LCM of 1456 and 1460.

LCM(1456,1460) = 24×51×71×131×731
LCM(1456,1460) = 531440

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

Factors of 1460

List of positive integer factors of 1460 that divides 1460 without a remainder.

1, 2, 4, 5, 10, 20, 73, 146, 292, 365, 730, 1460

Least Common Multiple of 1456 and 1460 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1456 and 1460, than apply into the LCM equation.

GCF(1456,1460) = 4
LCM(1456,1460) = ( 1456 × 1460) / 4
LCM(1456,1460) = 2125760 / 4
LCM(1456,1460) = 531440

Properties of LCM 1456 and 1460

(i) The LCM of 1460 and 1456 is associative

LCM of 1456 and 1460 = LCM of 1460 and 1456

Related Least Common Multiples of 1456

Related Least Common Multiples of 1460

Frequently Asked Questions on LCM of 1456 and 1460

1. What is the LCM of 1456 and 1460?

Answer: LCM of 1456 and 1460 is 531440.

2. 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.

3. What are the Factors of 1460?

Answer: Factors of 1460 are 1, 2, 4, 5, 10, 20, 73, 146, 292, 365, 730, 1460. There are 12 integers that are factors of 1460. The greatest factor of 1460 is 1460.

4. How to Find the LCM of 1456 and 1460?

Answer:

Least Common Multiple of 1456 and 1460 = 531440

Step 1: Find the prime factorization of 1456

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

Step 2: Find the prime factorization of 1460

1460 = 2 x 2 x 5 x 73

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

LCM = 531440 = 2 x 2 x 2 x 2 x 5 x 7 x 13 x 73

Step 4: Therefore, the least common multiple of 1456 and 1460 is 531440.