Least Common Multiple of 2992 and 3000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2992 and 3000 the smallest integer that is 1122000 that is divisible by both numbers.

Least Common Multiple (LCM) of 2992 and 3000 is 1122000.

LCM(2992,3000) = 1122000

LCM of 2992 and 3000

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

LCM of:
and

Least Common Multiple of 2992 and 3000

LCM of 2992 and 3000 is 1122000

Least common multiple can be found by multiplying the highest exponent prime factors of 2992 and 3000. First we will calculate the prime factors of 2992 and 3000.

Prime Factorization of 2992


2 2992
2 1496
2 748
2 374
11 187
17 17
1

Prime factors of 2992 are 2, 11,17. Prime factorization of 2992 in exponential form is:

2992 = 24×111×171

Prime Factorization of 3000


2 3000
2 1500
2 750
3 375
5 125
5 25
5 5
1

Prime factors of 3000 are 2, 3,5. Prime factorization of 3000 in exponential form is:

3000 = 23×31×53

Now multiplying the highest exponent prime factors to calculate the LCM of 2992 and 3000.

LCM(2992,3000) = 24×31×53×111×171
LCM(2992,3000) = 1122000

Factors of 2992

List of positive integer factors of 2992 that divides 2992 without a remainder.

1, 2, 4, 8, 11, 16, 17, 22, 34, 44, 68, 88, 136, 176, 187, 272, 374, 748, 1496, 2992

Factors of 3000

List of positive integer factors of 3000 that divides 3000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000

Least Common Multiple of 2992 and 3000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2992 and 3000, than apply into the LCM equation.

GCF(2992,3000) = 8
LCM(2992,3000) = ( 2992 × 3000) / 8
LCM(2992,3000) = 8976000 / 8
LCM(2992,3000) = 1122000

Properties of LCM 2992 and 3000

(i) The LCM of 3000 and 2992 is associative

LCM of 2992 and 3000 = LCM of 3000 and 2992

Related Least Common Multiples of 2992

Related Least Common Multiples of 3000

Frequently Asked Questions on LCM of 2992 and 3000

1. What is the LCM of 2992 and 3000?

Answer: LCM of 2992 and 3000 is 1122000.

2. What are the Factors of 2992?

Answer: Factors of 2992 are 1, 2, 4, 8, 11, 16, 17, 22, 34, 44, 68, 88, 136, 176, 187, 272, 374, 748, 1496, 2992. There are 20 integers that are factors of 2992. The greatest factor of 2992 is 2992.

3. What are the Factors of 3000?

Answer: Factors of 3000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000. There are 32 integers that are factors of 3000. The greatest factor of 3000 is 3000.

4. How to Find the LCM of 2992 and 3000?

Answer:

Least Common Multiple of 2992 and 3000 = 1122000

Step 1: Find the prime factorization of 2992

2992 = 2 x 2 x 2 x 2 x 11 x 17

Step 2: Find the prime factorization of 3000

3000 = 2 x 2 x 2 x 3 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 = 1122000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 11 x 17

Step 4: Therefore, the least common multiple of 2992 and 3000 is 1122000.