Least Common Multiple of 7996 and 8000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7996 and 8000 the smallest integer that is 15992000 that is divisible by both numbers.

Least Common Multiple (LCM) of 7996 and 8000 is 15992000.

LCM(7996,8000) = 15992000

LCM of 7996 and 8000

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

LCM of:
and

Least Common Multiple of 7996 and 8000

LCM of 7996 and 8000 is 15992000

Least common multiple can be found by multiplying the highest exponent prime factors of 7996 and 8000. First we will calculate the prime factors of 7996 and 8000.

Prime Factorization of 7996


2 7996
2 3998
1999 1999
1

Prime factors of 7996 are 2,1999. Prime factorization of 7996 in exponential form is:

7996 = 22×19991

Prime Factorization of 8000


2 8000
2 4000
2 2000
2 1000
2 500
2 250
5 125
5 25
5 5
1

Prime factors of 8000 are 2,5. Prime factorization of 8000 in exponential form is:

8000 = 26×53

Now multiplying the highest exponent prime factors to calculate the LCM of 7996 and 8000.

LCM(7996,8000) = 26×53×19991
LCM(7996,8000) = 15992000

Factors of 7996

List of positive integer factors of 7996 that divides 7996 without a remainder.

1, 2, 4, 1999, 3998, 7996

Factors of 8000

List of positive integer factors of 8000 that divides 8000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 800, 1000, 1600, 2000, 4000, 8000

Least Common Multiple of 7996 and 8000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7996 and 8000, than apply into the LCM equation.

GCF(7996,8000) = 4
LCM(7996,8000) = ( 7996 × 8000) / 4
LCM(7996,8000) = 63968000 / 4
LCM(7996,8000) = 15992000

Properties of LCM 7996 and 8000

(i) The LCM of 8000 and 7996 is associative

LCM of 7996 and 8000 = LCM of 8000 and 7996

Related Least Common Multiples of 7996

Related Least Common Multiples of 8000

Frequently Asked Questions on LCM of 7996 and 8000

1. What is the LCM of 7996 and 8000?

Answer: LCM of 7996 and 8000 is 15992000.

2. What are the Factors of 7996?

Answer: Factors of 7996 are 1, 2, 4, 1999, 3998, 7996. There are 6 integers that are factors of 7996. The greatest factor of 7996 is 7996.

3. What are the Factors of 8000?

Answer: Factors of 8000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 800, 1000, 1600, 2000, 4000, 8000. There are 28 integers that are factors of 8000. The greatest factor of 8000 is 8000.

4. How to Find the LCM of 7996 and 8000?

Answer:

Least Common Multiple of 7996 and 8000 = 15992000

Step 1: Find the prime factorization of 7996

7996 = 2 x 2 x 1999

Step 2: Find the prime factorization of 8000

8000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 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 = 15992000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 1999

Step 4: Therefore, the least common multiple of 7996 and 8000 is 15992000.