Least Common Multiple of 3993 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 3993 and 4000 the smallest integer that is 15972000 that is divisible by both numbers.

Least Common Multiple (LCM) of 3993 and 4000 is 15972000.

LCM(3993,4000) = 15972000

LCM of 3993 and 4000

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

LCM of:
and

Least Common Multiple of 3993 and 4000

LCM of 3993 and 4000 is 15972000

Least common multiple can be found by multiplying the highest exponent prime factors of 3993 and 4000. First we will calculate the prime factors of 3993 and 4000.

Prime Factorization of 3993


3 3993
11 1331
11 121
11 11
1

Prime factors of 3993 are 3,11. Prime factorization of 3993 in exponential form is:

3993 = 31×113

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 3993 and 4000.

LCM(3993,4000) = 25×31×53×113
LCM(3993,4000) = 15972000

Factors of 3993

List of positive integer factors of 3993 that divides 3993 without a remainder.

1, 3, 11, 33, 121, 363, 1331, 3993

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 3993 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 3993 and 4000, than apply into the LCM equation.

GCF(3993,4000) = 1
LCM(3993,4000) = ( 3993 × 4000) / 1
LCM(3993,4000) = 15972000 / 1
LCM(3993,4000) = 15972000

Properties of LCM 3993 and 4000

(i) The LCM of 4000 and 3993 is associative

LCM of 3993 and 4000 = LCM of 4000 and 3993

Related Least Common Multiples of 3993

Related Least Common Multiples of 4000

Frequently Asked Questions on LCM of 3993 and 4000

1. What is the LCM of 3993 and 4000?

Answer: LCM of 3993 and 4000 is 15972000.

2. What are the Factors of 3993?

Answer: Factors of 3993 are 1, 3, 11, 33, 121, 363, 1331, 3993. There are 8 integers that are factors of 3993. The greatest factor of 3993 is 3993.

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 3993 and 4000?

Answer:

Least Common Multiple of 3993 and 4000 = 15972000

Step 1: Find the prime factorization of 3993

3993 = 3 x 11 x 11 x 11

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 = 15972000 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 11 x 11 x 11

Step 4: Therefore, the least common multiple of 3993 and 4000 is 15972000.