Least Common Multiple of 1530 and 1538

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 1538 the smallest integer that is 1176570 that is divisible by both numbers.

Least Common Multiple (LCM) of 1530 and 1538 is 1176570.

LCM(1530,1538) = 1176570

LCM of 1530 and 1538

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

LCM of:
and

Least Common Multiple of 1530 and 1538

LCM of 1530 and 1538 is 1176570

Least common multiple can be found by multiplying the highest exponent prime factors of 1530 and 1538. First we will calculate the prime factors of 1530 and 1538.

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 1538


2 1538
769 769
1

Prime factors of 1538 are 2,769. Prime factorization of 1538 in exponential form is:

1538 = 21×7691

Now multiplying the highest exponent prime factors to calculate the LCM of 1530 and 1538.

LCM(1530,1538) = 21×32×51×171×7691
LCM(1530,1538) = 1176570

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 1538

List of positive integer factors of 1538 that divides 1538 without a remainder.

1, 2, 769, 1538

Least Common Multiple of 1530 and 1538 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 1538, than apply into the LCM equation.

GCF(1530,1538) = 2
LCM(1530,1538) = ( 1530 × 1538) / 2
LCM(1530,1538) = 2353140 / 2
LCM(1530,1538) = 1176570

Properties of LCM 1530 and 1538

(i) The LCM of 1538 and 1530 is associative

LCM of 1530 and 1538 = LCM of 1538 and 1530

Related Least Common Multiples of 1530

Related Least Common Multiples of 1538

Frequently Asked Questions on LCM of 1530 and 1538

1. What is the LCM of 1530 and 1538?

Answer: LCM of 1530 and 1538 is 1176570.

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 1538?

Answer: Factors of 1538 are 1, 2, 769, 1538. There are 4 integers that are factors of 1538. The greatest factor of 1538 is 1538.

4. How to Find the LCM of 1530 and 1538?

Answer:

Least Common Multiple of 1530 and 1538 = 1176570

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 1538

1538 = 2 x 769

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

LCM = 1176570 = 2 x 3 x 3 x 5 x 17 x 769

Step 4: Therefore, the least common multiple of 1530 and 1538 is 1176570.