Least Common Multiple of 1524 and 1530

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1524 and 1530 the smallest integer that is 388620 that is divisible by both numbers.

Least Common Multiple (LCM) of 1524 and 1530 is 388620.

LCM(1524,1530) = 388620

LCM of 1524 and 1530

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

LCM of:
and

Least Common Multiple of 1524 and 1530

LCM of 1524 and 1530 is 388620

Least common multiple can be found by multiplying the highest exponent prime factors of 1524 and 1530. First we will calculate the prime factors of 1524 and 1530.

Prime Factorization of 1524


2 1524
2 762
3 381
127 127
1

Prime factors of 1524 are 2, 3,127. Prime factorization of 1524 in exponential form is:

1524 = 22×31×1271

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1524 and 1530.

LCM(1524,1530) = 22×32×51×171×1271
LCM(1524,1530) = 388620

Factors of 1524

List of positive integer factors of 1524 that divides 1524 without a remainder.

1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, 1524

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

Least Common Multiple of 1524 and 1530 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1524 and 1530, than apply into the LCM equation.

GCF(1524,1530) = 6
LCM(1524,1530) = ( 1524 × 1530) / 6
LCM(1524,1530) = 2331720 / 6
LCM(1524,1530) = 388620

Properties of LCM 1524 and 1530

(i) The LCM of 1530 and 1524 is associative

LCM of 1524 and 1530 = LCM of 1530 and 1524

Related Least Common Multiples of 1524

Related Least Common Multiples of 1530

Frequently Asked Questions on LCM of 1524 and 1530

1. What is the LCM of 1524 and 1530?

Answer: LCM of 1524 and 1530 is 388620.

2. What are the Factors of 1524?

Answer: Factors of 1524 are 1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, 1524. There are 12 integers that are factors of 1524. The greatest factor of 1524 is 1524.

3. 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.

4. How to Find the LCM of 1524 and 1530?

Answer:

Least Common Multiple of 1524 and 1530 = 388620

Step 1: Find the prime factorization of 1524

1524 = 2 x 2 x 3 x 127

Step 2: Find the prime factorization of 1530

1530 = 2 x 3 x 3 x 5 x 17

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

LCM = 388620 = 2 x 2 x 3 x 3 x 5 x 17 x 127

Step 4: Therefore, the least common multiple of 1524 and 1530 is 388620.