Least Common Multiple of 997 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 997 and 1000 the smallest integer that is 997000 that is divisible by both numbers.

Least Common Multiple (LCM) of 997 and 1000 is 997000.

LCM(997,1000) = 997000

LCM of 997 and 1000

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

LCM of:
and

Least Common Multiple of 997 and 1000

LCM of 997 and 1000 is 997000

Least common multiple can be found by multiplying the highest exponent prime factors of 997 and 1000. First we will calculate the prime factors of 997 and 1000.

Prime Factorization of 997


997 997
1

Prime factors of 997 are 997. Prime factorization of 997 in exponential form is:

997 = 9971

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 997 and 1000.

LCM(997,1000) = 23×53×9971
LCM(997,1000) = 997000

Factors of 997

List of positive integer factors of 997 that divides 997 without a remainder.

1, 997

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 997 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 997 and 1000, than apply into the LCM equation.

GCF(997,1000) = 1
LCM(997,1000) = ( 997 × 1000) / 1
LCM(997,1000) = 997000 / 1
LCM(997,1000) = 997000

Properties of LCM 997 and 1000

(i) The LCM of 1000 and 997 is associative

LCM of 997 and 1000 = LCM of 1000 and 997

Related Least Common Multiples of 997

Related Least Common Multiples of 1000

Frequently Asked Questions on LCM of 997 and 1000

1. What is the LCM of 997 and 1000?

Answer: LCM of 997 and 1000 is 997000.

2. What are the Factors of 997?

Answer: Factors of 997 are 1, 997. There are 2 integers that are factors of 997. The greatest factor of 997 is 997.

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 997 and 1000?

Answer:

Least Common Multiple of 997 and 1000 = 997000

Step 1: Find the prime factorization of 997

997 = 997

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 = 997000 = 2 x 2 x 2 x 5 x 5 x 5 x 997

Step 4: Therefore, the least common multiple of 997 and 1000 is 997000.