Least Common Multiple of 1512 and 1520

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1512 and 1520 the smallest integer that is 287280 that is divisible by both numbers.

Least Common Multiple (LCM) of 1512 and 1520 is 287280.

LCM(1512,1520) = 287280

LCM of 1512 and 1520

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

LCM of:
and

Least Common Multiple of 1512 and 1520

LCM of 1512 and 1520 is 287280

Least common multiple can be found by multiplying the highest exponent prime factors of 1512 and 1520. First we will calculate the prime factors of 1512 and 1520.

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

Prime Factorization of 1520


2 1520
2 760
2 380
2 190
5 95
19 19
1

Prime factors of 1520 are 2, 5,19. Prime factorization of 1520 in exponential form is:

1520 = 24×51×191

Now multiplying the highest exponent prime factors to calculate the LCM of 1512 and 1520.

LCM(1512,1520) = 24×33×51×71×191
LCM(1512,1520) = 287280

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

Factors of 1520

List of positive integer factors of 1520 that divides 1520 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760, 1520

Least Common Multiple of 1512 and 1520 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1512 and 1520, than apply into the LCM equation.

GCF(1512,1520) = 8
LCM(1512,1520) = ( 1512 × 1520) / 8
LCM(1512,1520) = 2298240 / 8
LCM(1512,1520) = 287280

Properties of LCM 1512 and 1520

(i) The LCM of 1520 and 1512 is associative

LCM of 1512 and 1520 = LCM of 1520 and 1512

Related Least Common Multiples of 1512

Related Least Common Multiples of 1520

Frequently Asked Questions on LCM of 1512 and 1520

1. What is the LCM of 1512 and 1520?

Answer: LCM of 1512 and 1520 is 287280.

2. 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.

3. What are the Factors of 1520?

Answer: Factors of 1520 are 1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760, 1520. There are 20 integers that are factors of 1520. The greatest factor of 1520 is 1520.

4. How to Find the LCM of 1512 and 1520?

Answer:

Least Common Multiple of 1512 and 1520 = 287280

Step 1: Find the prime factorization of 1512

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

Step 2: Find the prime factorization of 1520

1520 = 2 x 2 x 2 x 2 x 5 x 19

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

LCM = 287280 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7 x 19

Step 4: Therefore, the least common multiple of 1512 and 1520 is 287280.