Least Common Multiple of 1530 and 1536

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1530 and 1536 the smallest integer that is 391680 that is divisible by both numbers.

Least Common Multiple (LCM) of 1530 and 1536 is 391680.

LCM(1530,1536) = 391680

LCM of 1530 and 1536

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

LCM of:
and

Least Common Multiple of 1530 and 1536

LCM of 1530 and 1536 is 391680

Least common multiple can be found by multiplying the highest exponent prime factors of 1530 and 1536. First we will calculate the prime factors of 1530 and 1536.

Prime Factorization of 1530


2 1530
3 765
3 255
5 85
17 17
1

Prime factors of 1530 are 2, 3, 5,17. Prime factorization of 1530 in exponential form is:

1530 = 21×32×51×171

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1530 and 1536.

LCM(1530,1536) = 29×32×51×171
LCM(1530,1536) = 391680

Factors of 1530

List of positive integer factors of 1530 that divides 1530 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765, 1530

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

Least Common Multiple of 1530 and 1536 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1530 and 1536, than apply into the LCM equation.

GCF(1530,1536) = 6
LCM(1530,1536) = ( 1530 × 1536) / 6
LCM(1530,1536) = 2350080 / 6
LCM(1530,1536) = 391680

Properties of LCM 1530 and 1536

(i) The LCM of 1536 and 1530 is associative

LCM of 1530 and 1536 = LCM of 1536 and 1530

Related Least Common Multiples of 1530

Related Least Common Multiples of 1536

Frequently Asked Questions on LCM of 1530 and 1536

1. What is the LCM of 1530 and 1536?

Answer: LCM of 1530 and 1536 is 391680.

2. What are the Factors of 1530?

Answer: Factors of 1530 are 1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765, 1530. There are 24 integers that are factors of 1530. The greatest factor of 1530 is 1530.

3. 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.

4. How to Find the LCM of 1530 and 1536?

Answer:

Least Common Multiple of 1530 and 1536 = 391680

Step 1: Find the prime factorization of 1530

1530 = 2 x 3 x 3 x 5 x 17

Step 2: 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 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 391680 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 1530 and 1536 is 391680.