Least Common Multiple of 1536 and 1540

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1536 and 1540 the smallest integer that is 591360 that is divisible by both numbers.

Least Common Multiple (LCM) of 1536 and 1540 is 591360.

LCM(1536,1540) = 591360

LCM of 1536 and 1540

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

LCM of:
and

Least Common Multiple of 1536 and 1540

LCM of 1536 and 1540 is 591360

Least common multiple can be found by multiplying the highest exponent prime factors of 1536 and 1540. First we will calculate the prime factors of 1536 and 1540.

Prime Factorization of 1536


2 1536
2 768
2 384
2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 1536 are 2,3. Prime factorization of 1536 in exponential form is:

1536 = 29×31

Prime Factorization of 1540


2 1540
2 770
5 385
7 77
11 11
1

Prime factors of 1540 are 2, 5, 7,11. Prime factorization of 1540 in exponential form is:

1540 = 22×51×71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 1536 and 1540.

LCM(1536,1540) = 29×31×51×71×111
LCM(1536,1540) = 591360

Factors of 1536

List of positive integer factors of 1536 that divides 1536 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536

Factors of 1540

List of positive integer factors of 1540 that divides 1540 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540

Least Common Multiple of 1536 and 1540 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1536 and 1540, than apply into the LCM equation.

GCF(1536,1540) = 4
LCM(1536,1540) = ( 1536 × 1540) / 4
LCM(1536,1540) = 2365440 / 4
LCM(1536,1540) = 591360

Properties of LCM 1536 and 1540

(i) The LCM of 1540 and 1536 is associative

LCM of 1536 and 1540 = LCM of 1540 and 1536

Related Least Common Multiples of 1536

Related Least Common Multiples of 1540

Frequently Asked Questions on LCM of 1536 and 1540

1. What is the LCM of 1536 and 1540?

Answer: LCM of 1536 and 1540 is 591360.

2. What are the Factors of 1536?

Answer: Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536. There are 20 integers that are factors of 1536. The greatest factor of 1536 is 1536.

3. What are the Factors of 1540?

Answer: Factors of 1540 are 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540. There are 24 integers that are factors of 1540. The greatest factor of 1540 is 1540.

4. How to Find the LCM of 1536 and 1540?

Answer:

Least Common Multiple of 1536 and 1540 = 591360

Step 1: Find the prime factorization of 1536

1536 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 1540

1540 = 2 x 2 x 5 x 7 x 11

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

LCM = 591360 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 11

Step 4: Therefore, the least common multiple of 1536 and 1540 is 591360.