Least Common Multiple of 992 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 992 and 1000 the smallest integer that is 124000 that is divisible by both numbers.

Least Common Multiple (LCM) of 992 and 1000 is 124000.

LCM(992,1000) = 124000

LCM of 992 and 1000

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

LCM of:
and

Least Common Multiple of 992 and 1000

LCM of 992 and 1000 is 124000

Least common multiple can be found by multiplying the highest exponent prime factors of 992 and 1000. First we will calculate the prime factors of 992 and 1000.

Prime Factorization of 992


2 992
2 496
2 248
2 124
2 62
31 31
1

Prime factors of 992 are 2,31. Prime factorization of 992 in exponential form is:

992 = 25×311

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 992 and 1000.

LCM(992,1000) = 25×53×311
LCM(992,1000) = 124000

Factors of 992

List of positive integer factors of 992 that divides 992 without a remainder.

1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992

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 992 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 992 and 1000, than apply into the LCM equation.

GCF(992,1000) = 8
LCM(992,1000) = ( 992 × 1000) / 8
LCM(992,1000) = 992000 / 8
LCM(992,1000) = 124000

Properties of LCM 992 and 1000

(i) The LCM of 1000 and 992 is associative

LCM of 992 and 1000 = LCM of 1000 and 992

Related Least Common Multiples of 992

Related Least Common Multiples of 1000

Frequently Asked Questions on LCM of 992 and 1000

1. What is the LCM of 992 and 1000?

Answer: LCM of 992 and 1000 is 124000.

2. What are the Factors of 992?

Answer: Factors of 992 are 1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992. There are 12 integers that are factors of 992. The greatest factor of 992 is 992.

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 992 and 1000?

Answer:

Least Common Multiple of 992 and 1000 = 124000

Step 1: Find the prime factorization of 992

992 = 2 x 2 x 2 x 2 x 2 x 31

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 = 124000 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 31

Step 4: Therefore, the least common multiple of 992 and 1000 is 124000.