Least Common Multiple of 5760 and 5767

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 5767 the smallest integer that is 33217920 that is divisible by both numbers.

Least Common Multiple (LCM) of 5760 and 5767 is 33217920.

LCM(5760,5767) = 33217920

LCM of 5760 and 5767

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

LCM of:
and

Least Common Multiple of 5760 and 5767

LCM of 5760 and 5767 is 33217920

Least common multiple can be found by multiplying the highest exponent prime factors of 5760 and 5767. First we will calculate the prime factors of 5760 and 5767.

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 5767


73 5767
79 79
1

Prime factors of 5767 are 73,79. Prime factorization of 5767 in exponential form is:

5767 = 731×791

Now multiplying the highest exponent prime factors to calculate the LCM of 5760 and 5767.

LCM(5760,5767) = 27×32×51×731×791
LCM(5760,5767) = 33217920

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 5767

List of positive integer factors of 5767 that divides 5767 without a remainder.

1, 73, 79, 5767

Least Common Multiple of 5760 and 5767 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 5767, than apply into the LCM equation.

GCF(5760,5767) = 1
LCM(5760,5767) = ( 5760 × 5767) / 1
LCM(5760,5767) = 33217920 / 1
LCM(5760,5767) = 33217920

Properties of LCM 5760 and 5767

(i) The LCM of 5767 and 5760 is associative

LCM of 5760 and 5767 = LCM of 5767 and 5760

Related Least Common Multiples of 5760

Related Least Common Multiples of 5767

Frequently Asked Questions on LCM of 5760 and 5767

1. What is the LCM of 5760 and 5767?

Answer: LCM of 5760 and 5767 is 33217920.

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 5767?

Answer: Factors of 5767 are 1, 73, 79, 5767. There are 4 integers that are factors of 5767. The greatest factor of 5767 is 5767.

4. How to Find the LCM of 5760 and 5767?

Answer:

Least Common Multiple of 5760 and 5767 = 33217920

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 5767

5767 = 73 x 79

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

LCM = 33217920 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 73 x 79

Step 4: Therefore, the least common multiple of 5760 and 5767 is 33217920.