Least Common Multiple of 6760 and 6768

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6760 and 6768 the smallest integer that is 5718960 that is divisible by both numbers.

Least Common Multiple (LCM) of 6760 and 6768 is 5718960.

LCM(6760,6768) = 5718960

LCM of 6760 and 6768

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

LCM of:
and

Least Common Multiple of 6760 and 6768

LCM of 6760 and 6768 is 5718960

Least common multiple can be found by multiplying the highest exponent prime factors of 6760 and 6768. First we will calculate the prime factors of 6760 and 6768.

Prime Factorization of 6760


2 6760
2 3380
2 1690
5 845
13 169
13 13
1

Prime factors of 6760 are 2, 5,13. Prime factorization of 6760 in exponential form is:

6760 = 23×51×132

Prime Factorization of 6768


2 6768
2 3384
2 1692
2 846
3 423
3 141
47 47
1

Prime factors of 6768 are 2, 3,47. Prime factorization of 6768 in exponential form is:

6768 = 24×32×471

Now multiplying the highest exponent prime factors to calculate the LCM of 6760 and 6768.

LCM(6760,6768) = 24×32×51×132×471
LCM(6760,6768) = 5718960

Factors of 6760

List of positive integer factors of 6760 that divides 6760 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 169, 260, 338, 520, 676, 845, 1352, 1690, 3380, 6760

Factors of 6768

List of positive integer factors of 6768 that divides 6768 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 47, 48, 72, 94, 141, 144, 188, 282, 376, 423, 564, 752, 846, 1128, 1692, 2256, 3384, 6768

Least Common Multiple of 6760 and 6768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6760 and 6768, than apply into the LCM equation.

GCF(6760,6768) = 8
LCM(6760,6768) = ( 6760 × 6768) / 8
LCM(6760,6768) = 45751680 / 8
LCM(6760,6768) = 5718960

Properties of LCM 6760 and 6768

(i) The LCM of 6768 and 6760 is associative

LCM of 6760 and 6768 = LCM of 6768 and 6760

Related Least Common Multiples of 6760

Related Least Common Multiples of 6768

Frequently Asked Questions on LCM of 6760 and 6768

1. What is the LCM of 6760 and 6768?

Answer: LCM of 6760 and 6768 is 5718960.

2. What are the Factors of 6760?

Answer: Factors of 6760 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 169, 260, 338, 520, 676, 845, 1352, 1690, 3380, 6760. There are 24 integers that are factors of 6760. The greatest factor of 6760 is 6760.

3. What are the Factors of 6768?

Answer: Factors of 6768 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 47, 48, 72, 94, 141, 144, 188, 282, 376, 423, 564, 752, 846, 1128, 1692, 2256, 3384, 6768. There are 30 integers that are factors of 6768. The greatest factor of 6768 is 6768.

4. How to Find the LCM of 6760 and 6768?

Answer:

Least Common Multiple of 6760 and 6768 = 5718960

Step 1: Find the prime factorization of 6760

6760 = 2 x 2 x 2 x 5 x 13 x 13

Step 2: Find the prime factorization of 6768

6768 = 2 x 2 x 2 x 2 x 3 x 3 x 47

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

LCM = 5718960 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 13 x 13 x 47

Step 4: Therefore, the least common multiple of 6760 and 6768 is 5718960.