Least Common Multiple of 1992 and 2000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1992 and 2000 the smallest integer that is 498000 that is divisible by both numbers.

Least Common Multiple (LCM) of 1992 and 2000 is 498000.

LCM(1992,2000) = 498000

LCM of 1992 and 2000

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

LCM of:
and

Least Common Multiple of 1992 and 2000

LCM of 1992 and 2000 is 498000

Least common multiple can be found by multiplying the highest exponent prime factors of 1992 and 2000. First we will calculate the prime factors of 1992 and 2000.

Prime Factorization of 1992


2 1992
2 996
2 498
3 249
83 83
1

Prime factors of 1992 are 2, 3,83. Prime factorization of 1992 in exponential form is:

1992 = 23×31×831

Prime Factorization of 2000


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

Prime factors of 2000 are 2,5. Prime factorization of 2000 in exponential form is:

2000 = 24×53

Now multiplying the highest exponent prime factors to calculate the LCM of 1992 and 2000.

LCM(1992,2000) = 24×31×53×831
LCM(1992,2000) = 498000

Factors of 1992

List of positive integer factors of 1992 that divides 1992 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 83, 166, 249, 332, 498, 664, 996, 1992

Factors of 2000

List of positive integer factors of 2000 that divides 2000 without a remainder.

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

Least Common Multiple of 1992 and 2000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1992 and 2000, than apply into the LCM equation.

GCF(1992,2000) = 8
LCM(1992,2000) = ( 1992 × 2000) / 8
LCM(1992,2000) = 3984000 / 8
LCM(1992,2000) = 498000

Properties of LCM 1992 and 2000

(i) The LCM of 2000 and 1992 is associative

LCM of 1992 and 2000 = LCM of 2000 and 1992

Related Least Common Multiples of 1992

Related Least Common Multiples of 2000

Frequently Asked Questions on LCM of 1992 and 2000

1. What is the LCM of 1992 and 2000?

Answer: LCM of 1992 and 2000 is 498000.

2. What are the Factors of 1992?

Answer: Factors of 1992 are 1, 2, 3, 4, 6, 8, 12, 24, 83, 166, 249, 332, 498, 664, 996, 1992. There are 16 integers that are factors of 1992. The greatest factor of 1992 is 1992.

3. What are the Factors of 2000?

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

4. How to Find the LCM of 1992 and 2000?

Answer:

Least Common Multiple of 1992 and 2000 = 498000

Step 1: Find the prime factorization of 1992

1992 = 2 x 2 x 2 x 3 x 83

Step 2: Find the prime factorization of 2000

2000 = 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 = 498000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 83

Step 4: Therefore, the least common multiple of 1992 and 2000 is 498000.