Least Common Multiple of 6714 and 6720

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6714 and 6720 the smallest integer that is 7519680 that is divisible by both numbers.

Least Common Multiple (LCM) of 6714 and 6720 is 7519680.

LCM(6714,6720) = 7519680

LCM of 6714 and 6720

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

LCM of:
and

Least Common Multiple of 6714 and 6720

LCM of 6714 and 6720 is 7519680

Least common multiple can be found by multiplying the highest exponent prime factors of 6714 and 6720. First we will calculate the prime factors of 6714 and 6720.

Prime Factorization of 6714


2 6714
3 3357
3 1119
373 373
1

Prime factors of 6714 are 2, 3,373. Prime factorization of 6714 in exponential form is:

6714 = 21×32×3731

Prime Factorization of 6720


2 6720
2 3360
2 1680
2 840
2 420
2 210
3 105
5 35
7 7
1

Prime factors of 6720 are 2, 3, 5,7. Prime factorization of 6720 in exponential form is:

6720 = 26×31×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 6714 and 6720.

LCM(6714,6720) = 26×32×51×71×3731
LCM(6714,6720) = 7519680

Factors of 6714

List of positive integer factors of 6714 that divides 6714 without a remainder.

1, 2, 3, 6, 9, 18, 373, 746, 1119, 2238, 3357, 6714

Factors of 6720

List of positive integer factors of 6720 that divides 6720 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 192, 210, 224, 240, 280, 320, 336, 420, 448, 480, 560, 672, 840, 960, 1120, 1344, 1680, 2240, 3360, 6720

Least Common Multiple of 6714 and 6720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6714 and 6720, than apply into the LCM equation.

GCF(6714,6720) = 6
LCM(6714,6720) = ( 6714 × 6720) / 6
LCM(6714,6720) = 45118080 / 6
LCM(6714,6720) = 7519680

Properties of LCM 6714 and 6720

(i) The LCM of 6720 and 6714 is associative

LCM of 6714 and 6720 = LCM of 6720 and 6714

Related Least Common Multiples of 6714

Related Least Common Multiples of 6720

Frequently Asked Questions on LCM of 6714 and 6720

1. What is the LCM of 6714 and 6720?

Answer: LCM of 6714 and 6720 is 7519680.

2. What are the Factors of 6714?

Answer: Factors of 6714 are 1, 2, 3, 6, 9, 18, 373, 746, 1119, 2238, 3357, 6714. There are 12 integers that are factors of 6714. The greatest factor of 6714 is 6714.

3. What are the Factors of 6720?

Answer: Factors of 6720 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 64, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 192, 210, 224, 240, 280, 320, 336, 420, 448, 480, 560, 672, 840, 960, 1120, 1344, 1680, 2240, 3360, 6720. There are 56 integers that are factors of 6720. The greatest factor of 6720 is 6720.

4. How to Find the LCM of 6714 and 6720?

Answer:

Least Common Multiple of 6714 and 6720 = 7519680

Step 1: Find the prime factorization of 6714

6714 = 2 x 3 x 3 x 373

Step 2: Find the prime factorization of 6720

6720 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7

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

LCM = 7519680 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 373

Step 4: Therefore, the least common multiple of 6714 and 6720 is 7519680.