Least Common Multiple of 1506 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 1506 and 1512 the smallest integer that is 379512 that is divisible by both numbers.

Least Common Multiple (LCM) of 1506 and 1512 is 379512.

LCM(1506,1512) = 379512

LCM of 1506 and 1512

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

LCM of:
and

Least Common Multiple of 1506 and 1512

LCM of 1506 and 1512 is 379512

Least common multiple can be found by multiplying the highest exponent prime factors of 1506 and 1512. First we will calculate the prime factors of 1506 and 1512.

Prime Factorization of 1506


2 1506
3 753
251 251
1

Prime factors of 1506 are 2, 3,251. Prime factorization of 1506 in exponential form is:

1506 = 21×31×2511

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 1506 and 1512.

LCM(1506,1512) = 23×33×71×2511
LCM(1506,1512) = 379512

Factors of 1506

List of positive integer factors of 1506 that divides 1506 without a remainder.

1, 2, 3, 6, 251, 502, 753, 1506

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 1506 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 1506 and 1512, than apply into the LCM equation.

GCF(1506,1512) = 6
LCM(1506,1512) = ( 1506 × 1512) / 6
LCM(1506,1512) = 2277072 / 6
LCM(1506,1512) = 379512

Properties of LCM 1506 and 1512

(i) The LCM of 1512 and 1506 is associative

LCM of 1506 and 1512 = LCM of 1512 and 1506

Related Least Common Multiples of 1506

Related Least Common Multiples of 1512

Frequently Asked Questions on LCM of 1506 and 1512

1. What is the LCM of 1506 and 1512?

Answer: LCM of 1506 and 1512 is 379512.

2. What are the Factors of 1506?

Answer: Factors of 1506 are 1, 2, 3, 6, 251, 502, 753, 1506. There are 8 integers that are factors of 1506. The greatest factor of 1506 is 1506.

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 1506 and 1512?

Answer:

Least Common Multiple of 1506 and 1512 = 379512

Step 1: Find the prime factorization of 1506

1506 = 2 x 3 x 251

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 = 379512 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 251

Step 4: Therefore, the least common multiple of 1506 and 1512 is 379512.