Least Common Multiple of 7680 and 7686

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7680 and 7686 the smallest integer that is 9838080 that is divisible by both numbers.

Least Common Multiple (LCM) of 7680 and 7686 is 9838080.

LCM(7680,7686) = 9838080

LCM of 7680 and 7686

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

LCM of:
and

Least Common Multiple of 7680 and 7686

LCM of 7680 and 7686 is 9838080

Least common multiple can be found by multiplying the highest exponent prime factors of 7680 and 7686. First we will calculate the prime factors of 7680 and 7686.

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

Prime Factorization of 7686


2 7686
3 3843
3 1281
7 427
61 61
1

Prime factors of 7686 are 2, 3, 7,61. Prime factorization of 7686 in exponential form is:

7686 = 21×32×71×611

Now multiplying the highest exponent prime factors to calculate the LCM of 7680 and 7686.

LCM(7680,7686) = 29×32×51×71×611
LCM(7680,7686) = 9838080

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

Factors of 7686

List of positive integer factors of 7686 that divides 7686 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 61, 63, 122, 126, 183, 366, 427, 549, 854, 1098, 1281, 2562, 3843, 7686

Least Common Multiple of 7680 and 7686 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7680 and 7686, than apply into the LCM equation.

GCF(7680,7686) = 6
LCM(7680,7686) = ( 7680 × 7686) / 6
LCM(7680,7686) = 59028480 / 6
LCM(7680,7686) = 9838080

Properties of LCM 7680 and 7686

(i) The LCM of 7686 and 7680 is associative

LCM of 7680 and 7686 = LCM of 7686 and 7680

Related Least Common Multiples of 7680

Related Least Common Multiples of 7686

Frequently Asked Questions on LCM of 7680 and 7686

1. What is the LCM of 7680 and 7686?

Answer: LCM of 7680 and 7686 is 9838080.

2. 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.

3. What are the Factors of 7686?

Answer: Factors of 7686 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 61, 63, 122, 126, 183, 366, 427, 549, 854, 1098, 1281, 2562, 3843, 7686. There are 24 integers that are factors of 7686. The greatest factor of 7686 is 7686.

4. How to Find the LCM of 7680 and 7686?

Answer:

Least Common Multiple of 7680 and 7686 = 9838080

Step 1: 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 2: Find the prime factorization of 7686

7686 = 2 x 3 x 3 x 7 x 61

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

LCM = 9838080 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 61

Step 4: Therefore, the least common multiple of 7680 and 7686 is 9838080.