Least Common Multiple of 765 and 768

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 765 and 768 the smallest integer that is 195840 that is divisible by both numbers.

Least Common Multiple (LCM) of 765 and 768 is 195840.

LCM(765,768) = 195840

LCM of 765 and 768

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

LCM of:
and

Least Common Multiple of 765 and 768

LCM of 765 and 768 is 195840

Least common multiple can be found by multiplying the highest exponent prime factors of 765 and 768. First we will calculate the prime factors of 765 and 768.

Prime Factorization of 765


3 765
3 255
5 85
17 17
1

Prime factors of 765 are 3, 5,17. Prime factorization of 765 in exponential form is:

765 = 32×51×171

Prime Factorization of 768


2 768
2 384
2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 768 are 2,3. Prime factorization of 768 in exponential form is:

768 = 28×31

Now multiplying the highest exponent prime factors to calculate the LCM of 765 and 768.

LCM(765,768) = 28×32×51×171
LCM(765,768) = 195840

Factors of 765

List of positive integer factors of 765 that divides 765 without a remainder.

1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765

Factors of 768

List of positive integer factors of 768 that divides 768 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768

Least Common Multiple of 765 and 768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 765 and 768, than apply into the LCM equation.

GCF(765,768) = 3
LCM(765,768) = ( 765 × 768) / 3
LCM(765,768) = 587520 / 3
LCM(765,768) = 195840

Properties of LCM 765 and 768

(i) The LCM of 768 and 765 is associative

LCM of 765 and 768 = LCM of 768 and 765

Related Least Common Multiples of 765

Related Least Common Multiples of 768

Frequently Asked Questions on LCM of 765 and 768

1. What is the LCM of 765 and 768?

Answer: LCM of 765 and 768 is 195840.

2. What are the Factors of 765?

Answer: Factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765. There are 12 integers that are factors of 765. The greatest factor of 765 is 765.

3. What are the Factors of 768?

Answer: Factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768. There are 18 integers that are factors of 768. The greatest factor of 768 is 768.

4. How to Find the LCM of 765 and 768?

Answer:

Least Common Multiple of 765 and 768 = 195840

Step 1: Find the prime factorization of 765

765 = 3 x 3 x 5 x 17

Step 2: Find the prime factorization of 768

768 = 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 = 195840 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 17

Step 4: Therefore, the least common multiple of 765 and 768 is 195840.