Least Common Multiple of 7674 and 7680

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7674 and 7680 the smallest integer that is 9822720 that is divisible by both numbers.

Least Common Multiple (LCM) of 7674 and 7680 is 9822720.

LCM(7674,7680) = 9822720

LCM of 7674 and 7680

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

LCM of:
and

Least Common Multiple of 7674 and 7680

LCM of 7674 and 7680 is 9822720

Least common multiple can be found by multiplying the highest exponent prime factors of 7674 and 7680. First we will calculate the prime factors of 7674 and 7680.

Prime Factorization of 7674


2 7674
3 3837
1279 1279
1

Prime factors of 7674 are 2, 3,1279. Prime factorization of 7674 in exponential form is:

7674 = 21×31×12791

Prime Factorization of 7680


2 7680
2 3840
2 1920
2 960
2 480
2 240
2 120
2 60
2 30
3 15
5 5
1

Prime factors of 7680 are 2, 3,5. Prime factorization of 7680 in exponential form is:

7680 = 29×31×51

Now multiplying the highest exponent prime factors to calculate the LCM of 7674 and 7680.

LCM(7674,7680) = 29×31×51×12791
LCM(7674,7680) = 9822720

Factors of 7674

List of positive integer factors of 7674 that divides 7674 without a remainder.

1, 2, 3, 6, 1279, 2558, 3837, 7674

Factors of 7680

List of positive integer factors of 7680 that divides 7680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1280, 1536, 1920, 2560, 3840, 7680

Least Common Multiple of 7674 and 7680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7674 and 7680, than apply into the LCM equation.

GCF(7674,7680) = 6
LCM(7674,7680) = ( 7674 × 7680) / 6
LCM(7674,7680) = 58936320 / 6
LCM(7674,7680) = 9822720

Properties of LCM 7674 and 7680

(i) The LCM of 7680 and 7674 is associative

LCM of 7674 and 7680 = LCM of 7680 and 7674

Related Least Common Multiples of 7674

Related Least Common Multiples of 7680

Frequently Asked Questions on LCM of 7674 and 7680

1. What is the LCM of 7674 and 7680?

Answer: LCM of 7674 and 7680 is 9822720.

2. What are the Factors of 7674?

Answer: Factors of 7674 are 1, 2, 3, 6, 1279, 2558, 3837, 7674. There are 8 integers that are factors of 7674. The greatest factor of 7674 is 7674.

3. What are the Factors of 7680?

Answer: Factors of 7680 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1280, 1536, 1920, 2560, 3840, 7680. There are 40 integers that are factors of 7680. The greatest factor of 7680 is 7680.

4. How to Find the LCM of 7674 and 7680?

Answer:

Least Common Multiple of 7674 and 7680 = 9822720

Step 1: Find the prime factorization of 7674

7674 = 2 x 3 x 1279

Step 2: Find the prime factorization of 7680

7680 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5

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

LCM = 9822720 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 1279

Step 4: Therefore, the least common multiple of 7674 and 7680 is 9822720.