Least Common Multiple of 1509 and 1512

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1509 and 1512 the smallest integer that is 760536 that is divisible by both numbers.

Least Common Multiple (LCM) of 1509 and 1512 is 760536.

LCM(1509,1512) = 760536

LCM of 1509 and 1512

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

LCM of:
and

Least Common Multiple of 1509 and 1512

LCM of 1509 and 1512 is 760536

Least common multiple can be found by multiplying the highest exponent prime factors of 1509 and 1512. First we will calculate the prime factors of 1509 and 1512.

Prime Factorization of 1509


3 1509
503 503
1

Prime factors of 1509 are 3,503. Prime factorization of 1509 in exponential form is:

1509 = 31×5031

Prime Factorization of 1512


2 1512
2 756
2 378
3 189
3 63
3 21
7 7
1

Prime factors of 1512 are 2, 3,7. Prime factorization of 1512 in exponential form is:

1512 = 23×33×71

Now multiplying the highest exponent prime factors to calculate the LCM of 1509 and 1512.

LCM(1509,1512) = 23×33×71×5031
LCM(1509,1512) = 760536

Factors of 1509

List of positive integer factors of 1509 that divides 1509 without a remainder.

1, 3, 503, 1509

Factors of 1512

List of positive integer factors of 1512 that divides 1512 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512

Least Common Multiple of 1509 and 1512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1509 and 1512, than apply into the LCM equation.

GCF(1509,1512) = 3
LCM(1509,1512) = ( 1509 × 1512) / 3
LCM(1509,1512) = 2281608 / 3
LCM(1509,1512) = 760536

Properties of LCM 1509 and 1512

(i) The LCM of 1512 and 1509 is associative

LCM of 1509 and 1512 = LCM of 1512 and 1509

Related Least Common Multiples of 1509

Related Least Common Multiples of 1512

Frequently Asked Questions on LCM of 1509 and 1512

1. What is the LCM of 1509 and 1512?

Answer: LCM of 1509 and 1512 is 760536.

2. What are the Factors of 1509?

Answer: Factors of 1509 are 1, 3, 503, 1509. There are 4 integers that are factors of 1509. The greatest factor of 1509 is 1509.

3. What are the Factors of 1512?

Answer: Factors of 1512 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512. There are 32 integers that are factors of 1512. The greatest factor of 1512 is 1512.

4. How to Find the LCM of 1509 and 1512?

Answer:

Least Common Multiple of 1509 and 1512 = 760536

Step 1: Find the prime factorization of 1509

1509 = 3 x 503

Step 2: Find the prime factorization of 1512

1512 = 2 x 2 x 2 x 3 x 3 x 3 x 7

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

LCM = 760536 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 503

Step 4: Therefore, the least common multiple of 1509 and 1512 is 760536.