Least Common Multiple of 996 and 1000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 996 and 1000 the smallest integer that is 249000 that is divisible by both numbers.

Least Common Multiple (LCM) of 996 and 1000 is 249000.

LCM(996,1000) = 249000

LCM of 996 and 1000

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

LCM of:
and

Least Common Multiple of 996 and 1000

LCM of 996 and 1000 is 249000

Least common multiple can be found by multiplying the highest exponent prime factors of 996 and 1000. First we will calculate the prime factors of 996 and 1000.

Prime Factorization of 996


2 996
2 498
3 249
83 83
1

Prime factors of 996 are 2, 3,83. Prime factorization of 996 in exponential form is:

996 = 22×31×831

Prime Factorization of 1000


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

Prime factors of 1000 are 2,5. Prime factorization of 1000 in exponential form is:

1000 = 23×53

Now multiplying the highest exponent prime factors to calculate the LCM of 996 and 1000.

LCM(996,1000) = 23×31×53×831
LCM(996,1000) = 249000

Factors of 996

List of positive integer factors of 996 that divides 996 without a remainder.

1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996

Factors of 1000

List of positive integer factors of 1000 that divides 1000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

Least Common Multiple of 996 and 1000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 996 and 1000, than apply into the LCM equation.

GCF(996,1000) = 4
LCM(996,1000) = ( 996 × 1000) / 4
LCM(996,1000) = 996000 / 4
LCM(996,1000) = 249000

Properties of LCM 996 and 1000

(i) The LCM of 1000 and 996 is associative

LCM of 996 and 1000 = LCM of 1000 and 996

Related Least Common Multiples of 996

Related Least Common Multiples of 1000

Frequently Asked Questions on LCM of 996 and 1000

1. What is the LCM of 996 and 1000?

Answer: LCM of 996 and 1000 is 249000.

2. What are the Factors of 996?

Answer: Factors of 996 are 1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996. There are 12 integers that are factors of 996. The greatest factor of 996 is 996.

3. What are the Factors of 1000?

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

4. How to Find the LCM of 996 and 1000?

Answer:

Least Common Multiple of 996 and 1000 = 249000

Step 1: Find the prime factorization of 996

996 = 2 x 2 x 3 x 83

Step 2: Find the prime factorization of 1000

1000 = 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 = 249000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 83

Step 4: Therefore, the least common multiple of 996 and 1000 is 249000.