Least Common Multiple of 5304 and 5312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5304 and 5312 the smallest integer that is 3521856 that is divisible by both numbers.

Least Common Multiple (LCM) of 5304 and 5312 is 3521856.

LCM(5304,5312) = 3521856

LCM of 5304 and 5312

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

LCM of:
and

Least Common Multiple of 5304 and 5312

LCM of 5304 and 5312 is 3521856

Least common multiple can be found by multiplying the highest exponent prime factors of 5304 and 5312. First we will calculate the prime factors of 5304 and 5312.

Prime Factorization of 5304


2 5304
2 2652
2 1326
3 663
13 221
17 17
1

Prime factors of 5304 are 2, 3, 13,17. Prime factorization of 5304 in exponential form is:

5304 = 23×31×131×171

Prime Factorization of 5312


2 5312
2 2656
2 1328
2 664
2 332
2 166
83 83
1

Prime factors of 5312 are 2,83. Prime factorization of 5312 in exponential form is:

5312 = 26×831

Now multiplying the highest exponent prime factors to calculate the LCM of 5304 and 5312.

LCM(5304,5312) = 26×31×131×171×831
LCM(5304,5312) = 3521856

Factors of 5304

List of positive integer factors of 5304 that divides 5304 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 17, 24, 26, 34, 39, 51, 52, 68, 78, 102, 104, 136, 156, 204, 221, 312, 408, 442, 663, 884, 1326, 1768, 2652, 5304

Factors of 5312

List of positive integer factors of 5312 that divides 5312 without a remainder.

1, 2, 4, 8, 16, 32, 64, 83, 166, 332, 664, 1328, 2656, 5312

Least Common Multiple of 5304 and 5312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5304 and 5312, than apply into the LCM equation.

GCF(5304,5312) = 8
LCM(5304,5312) = ( 5304 × 5312) / 8
LCM(5304,5312) = 28174848 / 8
LCM(5304,5312) = 3521856

Properties of LCM 5304 and 5312

(i) The LCM of 5312 and 5304 is associative

LCM of 5304 and 5312 = LCM of 5312 and 5304

Related Least Common Multiples of 5304

Related Least Common Multiples of 5312

Frequently Asked Questions on LCM of 5304 and 5312

1. What is the LCM of 5304 and 5312?

Answer: LCM of 5304 and 5312 is 3521856.

2. What are the Factors of 5304?

Answer: Factors of 5304 are 1, 2, 3, 4, 6, 8, 12, 13, 17, 24, 26, 34, 39, 51, 52, 68, 78, 102, 104, 136, 156, 204, 221, 312, 408, 442, 663, 884, 1326, 1768, 2652, 5304. There are 32 integers that are factors of 5304. The greatest factor of 5304 is 5304.

3. What are the Factors of 5312?

Answer: Factors of 5312 are 1, 2, 4, 8, 16, 32, 64, 83, 166, 332, 664, 1328, 2656, 5312. There are 14 integers that are factors of 5312. The greatest factor of 5312 is 5312.

4. How to Find the LCM of 5304 and 5312?

Answer:

Least Common Multiple of 5304 and 5312 = 3521856

Step 1: Find the prime factorization of 5304

5304 = 2 x 2 x 2 x 3 x 13 x 17

Step 2: Find the prime factorization of 5312

5312 = 2 x 2 x 2 x 2 x 2 x 2 x 83

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

LCM = 3521856 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 17 x 83

Step 4: Therefore, the least common multiple of 5304 and 5312 is 3521856.