Least Common Multiple of 5760 and 5765

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 5765 the smallest integer that is 6641280 that is divisible by both numbers.

Least Common Multiple (LCM) of 5760 and 5765 is 6641280.

LCM(5760,5765) = 6641280

LCM of 5760 and 5765

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

LCM of:
and

Least Common Multiple of 5760 and 5765

LCM of 5760 and 5765 is 6641280

Least common multiple can be found by multiplying the highest exponent prime factors of 5760 and 5765. First we will calculate the prime factors of 5760 and 5765.

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 5765


5 5765
1153 1153
1

Prime factors of 5765 are 5,1153. Prime factorization of 5765 in exponential form is:

5765 = 51×11531

Now multiplying the highest exponent prime factors to calculate the LCM of 5760 and 5765.

LCM(5760,5765) = 27×32×51×11531
LCM(5760,5765) = 6641280

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 5765

List of positive integer factors of 5765 that divides 5765 without a remainder.

1, 5, 1153, 5765

Least Common Multiple of 5760 and 5765 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 5765, than apply into the LCM equation.

GCF(5760,5765) = 5
LCM(5760,5765) = ( 5760 × 5765) / 5
LCM(5760,5765) = 33206400 / 5
LCM(5760,5765) = 6641280

Properties of LCM 5760 and 5765

(i) The LCM of 5765 and 5760 is associative

LCM of 5760 and 5765 = LCM of 5765 and 5760

Related Least Common Multiples of 5760

Related Least Common Multiples of 5765

Frequently Asked Questions on LCM of 5760 and 5765

1. What is the LCM of 5760 and 5765?

Answer: LCM of 5760 and 5765 is 6641280.

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 5765?

Answer: Factors of 5765 are 1, 5, 1153, 5765. There are 4 integers that are factors of 5765. The greatest factor of 5765 is 5765.

4. How to Find the LCM of 5760 and 5765?

Answer:

Least Common Multiple of 5760 and 5765 = 6641280

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 5765

5765 = 5 x 1153

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

LCM = 6641280 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 1153

Step 4: Therefore, the least common multiple of 5760 and 5765 is 6641280.