Least Common Multiple of 3992 and 4000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3992 and 4000 the smallest integer that is 1996000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3992 and 4000 is 1996000.

LCM(3992,4000) = 1996000

LCM of 3992 and 4000

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

LCM of:
and

Least Common Multiple of 3992 and 4000

LCM of 3992 and 4000 is 1996000

Least common multiple can be found by multiplying the highest exponent prime factors of 3992 and 4000. First we will calculate the prime factors of 3992 and 4000.

Prime Factorization of 3992


2 3992
2 1996
2 998
499 499
1

Prime factors of 3992 are 2,499. Prime factorization of 3992 in exponential form is:

3992 = 23×4991

Prime Factorization of 4000


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

Prime factors of 4000 are 2,5. Prime factorization of 4000 in exponential form is:

4000 = 25×53

Now multiplying the highest exponent prime factors to calculate the LCM of 3992 and 4000.

LCM(3992,4000) = 25×53×4991
LCM(3992,4000) = 1996000

Factors of 3992

List of positive integer factors of 3992 that divides 3992 without a remainder.

1, 2, 4, 8, 499, 998, 1996, 3992

Factors of 4000

List of positive integer factors of 4000 that divides 4000 without a remainder.

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

Least Common Multiple of 3992 and 4000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3992 and 4000, than apply into the LCM equation.

GCF(3992,4000) = 8
LCM(3992,4000) = ( 3992 × 4000) / 8
LCM(3992,4000) = 15968000 / 8
LCM(3992,4000) = 1996000

Properties of LCM 3992 and 4000

(i) The LCM of 4000 and 3992 is associative

LCM of 3992 and 4000 = LCM of 4000 and 3992

Related Least Common Multiples of 3992

Related Least Common Multiples of 4000

Frequently Asked Questions on LCM of 3992 and 4000

1. What is the LCM of 3992 and 4000?

Answer: LCM of 3992 and 4000 is 1996000.

2. What are the Factors of 3992?

Answer: Factors of 3992 are 1, 2, 4, 8, 499, 998, 1996, 3992. There are 8 integers that are factors of 3992. The greatest factor of 3992 is 3992.

3. What are the Factors of 4000?

Answer: Factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000. There are 24 integers that are factors of 4000. The greatest factor of 4000 is 4000.

4. How to Find the LCM of 3992 and 4000?

Answer:

Least Common Multiple of 3992 and 4000 = 1996000

Step 1: Find the prime factorization of 3992

3992 = 2 x 2 x 2 x 499

Step 2: Find the prime factorization of 4000

4000 = 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 = 1996000 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 499

Step 4: Therefore, the least common multiple of 3992 and 4000 is 1996000.