Least Common Multiple of 1528 and 1536

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 1528 and 1536 the smallest integer that is 293376 that is divisible by both numbers.

Least Common Multiple (LCM) of 1528 and 1536 is 293376.

LCM(1528,1536) = 293376

LCM of 1528 and 1536

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

LCM of:
and

Least Common Multiple of 1528 and 1536

LCM of 1528 and 1536 is 293376

Least common multiple can be found by multiplying the highest exponent prime factors of 1528 and 1536. First we will calculate the prime factors of 1528 and 1536.

Prime Factorization of 1528


2 1528
2 764
2 382
191 191
1

Prime factors of 1528 are 2,191. Prime factorization of 1528 in exponential form is:

1528 = 23×1911

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1528 and 1536.

LCM(1528,1536) = 29×31×1911
LCM(1528,1536) = 293376

Factors of 1528

List of positive integer factors of 1528 that divides 1528 without a remainder.

1, 2, 4, 8, 191, 382, 764, 1528

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

Least Common Multiple of 1528 and 1536 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1528 and 1536, than apply into the LCM equation.

GCF(1528,1536) = 8
LCM(1528,1536) = ( 1528 × 1536) / 8
LCM(1528,1536) = 2347008 / 8
LCM(1528,1536) = 293376

Properties of LCM 1528 and 1536

(i) The LCM of 1536 and 1528 is associative

LCM of 1528 and 1536 = LCM of 1536 and 1528

Frequently Asked Questions on LCM of 1528 and 1536

1. What is the LCM of 1528 and 1536?

Answer: LCM of 1528 and 1536 is 293376.

2. What are the Factors of 1528?

Answer: Factors of 1528 are 1, 2, 4, 8, 191, 382, 764, 1528. There are 8 integers that are factors of 1528. The greatest factor of 1528 is 1528.

3. 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.

4. How to Find the LCM of 1528 and 1536?

Answer:

Least Common Multiple of 1528 and 1536 = 293376

Step 1: Find the prime factorization of 1528

1528 = 2 x 2 x 2 x 191

Step 2: 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 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 293376 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 191

Step 4: Therefore, the least common multiple of 1528 and 1536 is 293376.