Least Common Multiple of 760 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 760 and 768 the smallest integer that is 72960 that is divisible by both numbers.

Least Common Multiple (LCM) of 760 and 768 is 72960.

LCM(760,768) = 72960

LCM of 760 and 768

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

LCM of:
and

Least Common Multiple of 760 and 768

LCM of 760 and 768 is 72960

Least common multiple can be found by multiplying the highest exponent prime factors of 760 and 768. First we will calculate the prime factors of 760 and 768.

Prime Factorization of 760


2 760
2 380
2 190
5 95
19 19
1

Prime factors of 760 are 2, 5,19. Prime factorization of 760 in exponential form is:

760 = 23×51×191

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 760 and 768.

LCM(760,768) = 28×31×51×191
LCM(760,768) = 72960

Factors of 760

List of positive integer factors of 760 that divides 760 without a remainder.

1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760

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 760 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 760 and 768, than apply into the LCM equation.

GCF(760,768) = 8
LCM(760,768) = ( 760 × 768) / 8
LCM(760,768) = 583680 / 8
LCM(760,768) = 72960

Properties of LCM 760 and 768

(i) The LCM of 768 and 760 is associative

LCM of 760 and 768 = LCM of 768 and 760

Related Least Common Multiples of 760

Related Least Common Multiples of 768

Frequently Asked Questions on LCM of 760 and 768

1. What is the LCM of 760 and 768?

Answer: LCM of 760 and 768 is 72960.

2. What are the Factors of 760?

Answer: Factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760. There are 16 integers that are factors of 760. The greatest factor of 760 is 760.

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 760 and 768?

Answer:

Least Common Multiple of 760 and 768 = 72960

Step 1: Find the prime factorization of 760

760 = 2 x 2 x 2 x 5 x 19

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 = 72960 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 19

Step 4: Therefore, the least common multiple of 760 and 768 is 72960.