Least Common Multiple of 5760 and 5768

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5760 and 5768 the smallest integer that is 4152960 that is divisible by both numbers.

Least Common Multiple (LCM) of 5760 and 5768 is 4152960.

LCM(5760,5768) = 4152960

LCM of 5760 and 5768

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

LCM of:
and

Least Common Multiple of 5760 and 5768

LCM of 5760 and 5768 is 4152960

Least common multiple can be found by multiplying the highest exponent prime factors of 5760 and 5768. First we will calculate the prime factors of 5760 and 5768.

Prime Factorization of 5760


2 5760
2 2880
2 1440
2 720
2 360
2 180
2 90
3 45
3 15
5 5
1

Prime factors of 5760 are 2, 3,5. Prime factorization of 5760 in exponential form is:

5760 = 27×32×51

Prime Factorization of 5768


2 5768
2 2884
2 1442
7 721
103 103
1

Prime factors of 5768 are 2, 7,103. Prime factorization of 5768 in exponential form is:

5768 = 23×71×1031

Now multiplying the highest exponent prime factors to calculate the LCM of 5760 and 5768.

LCM(5760,5768) = 27×32×51×71×1031
LCM(5760,5768) = 4152960

Factors of 5760

List of positive integer factors of 5760 that divides 5760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760

Factors of 5768

List of positive integer factors of 5768 that divides 5768 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 103, 206, 412, 721, 824, 1442, 2884, 5768

Least Common Multiple of 5760 and 5768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5760 and 5768, than apply into the LCM equation.

GCF(5760,5768) = 8
LCM(5760,5768) = ( 5760 × 5768) / 8
LCM(5760,5768) = 33223680 / 8
LCM(5760,5768) = 4152960

Properties of LCM 5760 and 5768

(i) The LCM of 5768 and 5760 is associative

LCM of 5760 and 5768 = LCM of 5768 and 5760

Related Least Common Multiples of 5760

Related Least Common Multiples of 5768

Frequently Asked Questions on LCM of 5760 and 5768

1. What is the LCM of 5760 and 5768?

Answer: LCM of 5760 and 5768 is 4152960.

2. What are the Factors of 5760?

Answer: Factors of 5760 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760. There are 48 integers that are factors of 5760. The greatest factor of 5760 is 5760.

3. What are the Factors of 5768?

Answer: Factors of 5768 are 1, 2, 4, 7, 8, 14, 28, 56, 103, 206, 412, 721, 824, 1442, 2884, 5768. There are 16 integers that are factors of 5768. The greatest factor of 5768 is 5768.

4. How to Find the LCM of 5760 and 5768?

Answer:

Least Common Multiple of 5760 and 5768 = 4152960

Step 1: Find the prime factorization of 5760

5760 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5

Step 2: Find the prime factorization of 5768

5768 = 2 x 2 x 2 x 7 x 103

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

LCM = 4152960 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 103

Step 4: Therefore, the least common multiple of 5760 and 5768 is 4152960.