Least Common Multiple of 1536 and 1542

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1536 and 1542 the smallest integer that is 394752 that is divisible by both numbers.

Least Common Multiple (LCM) of 1536 and 1542 is 394752.

LCM(1536,1542) = 394752

LCM of 1536 and 1542

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

LCM of:
and

Least Common Multiple of 1536 and 1542

LCM of 1536 and 1542 is 394752

Least common multiple can be found by multiplying the highest exponent prime factors of 1536 and 1542. First we will calculate the prime factors of 1536 and 1542.

Prime Factorization of 1536


2 1536
2 768
2 384
2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 1536 are 2,3. Prime factorization of 1536 in exponential form is:

1536 = 29×31

Prime Factorization of 1542


2 1542
3 771
257 257
1

Prime factors of 1542 are 2, 3,257. Prime factorization of 1542 in exponential form is:

1542 = 21×31×2571

Now multiplying the highest exponent prime factors to calculate the LCM of 1536 and 1542.

LCM(1536,1542) = 29×31×2571
LCM(1536,1542) = 394752

Factors of 1536

List of positive integer factors of 1536 that divides 1536 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536

Factors of 1542

List of positive integer factors of 1542 that divides 1542 without a remainder.

1, 2, 3, 6, 257, 514, 771, 1542

Least Common Multiple of 1536 and 1542 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1536 and 1542, than apply into the LCM equation.

GCF(1536,1542) = 6
LCM(1536,1542) = ( 1536 × 1542) / 6
LCM(1536,1542) = 2368512 / 6
LCM(1536,1542) = 394752

Properties of LCM 1536 and 1542

(i) The LCM of 1542 and 1536 is associative

LCM of 1536 and 1542 = LCM of 1542 and 1536

Related Least Common Multiples of 1536

Related Least Common Multiples of 1542

Frequently Asked Questions on LCM of 1536 and 1542

1. What is the LCM of 1536 and 1542?

Answer: LCM of 1536 and 1542 is 394752.

2. What are the Factors of 1536?

Answer: Factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536. There are 20 integers that are factors of 1536. The greatest factor of 1536 is 1536.

3. What are the Factors of 1542?

Answer: Factors of 1542 are 1, 2, 3, 6, 257, 514, 771, 1542. There are 8 integers that are factors of 1542. The greatest factor of 1542 is 1542.

4. How to Find the LCM of 1536 and 1542?

Answer:

Least Common Multiple of 1536 and 1542 = 394752

Step 1: Find the prime factorization of 1536

1536 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 1542

1542 = 2 x 3 x 257

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

LCM = 394752 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 257

Step 4: Therefore, the least common multiple of 1536 and 1542 is 394752.