Least Common Multiple of 6992 and 7000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6992 and 7000 the smallest integer that is 6118000 that is divisible by both numbers.

Least Common Multiple (LCM) of 6992 and 7000 is 6118000.

LCM(6992,7000) = 6118000

LCM of 6992 and 7000

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

LCM of:
and

Least Common Multiple of 6992 and 7000

LCM of 6992 and 7000 is 6118000

Least common multiple can be found by multiplying the highest exponent prime factors of 6992 and 7000. First we will calculate the prime factors of 6992 and 7000.

Prime Factorization of 6992


2 6992
2 3496
2 1748
2 874
19 437
23 23
1

Prime factors of 6992 are 2, 19,23. Prime factorization of 6992 in exponential form is:

6992 = 24×191×231

Prime Factorization of 7000


2 7000
2 3500
2 1750
5 875
5 175
5 35
7 7
1

Prime factors of 7000 are 2, 5,7. Prime factorization of 7000 in exponential form is:

7000 = 23×53×71

Now multiplying the highest exponent prime factors to calculate the LCM of 6992 and 7000.

LCM(6992,7000) = 24×53×71×191×231
LCM(6992,7000) = 6118000

Factors of 6992

List of positive integer factors of 6992 that divides 6992 without a remainder.

1, 2, 4, 8, 16, 19, 23, 38, 46, 76, 92, 152, 184, 304, 368, 437, 874, 1748, 3496, 6992

Factors of 7000

List of positive integer factors of 7000 that divides 7000 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000

Least Common Multiple of 6992 and 7000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6992 and 7000, than apply into the LCM equation.

GCF(6992,7000) = 8
LCM(6992,7000) = ( 6992 × 7000) / 8
LCM(6992,7000) = 48944000 / 8
LCM(6992,7000) = 6118000

Properties of LCM 6992 and 7000

(i) The LCM of 7000 and 6992 is associative

LCM of 6992 and 7000 = LCM of 7000 and 6992

Related Least Common Multiples of 6992

Related Least Common Multiples of 7000

Frequently Asked Questions on LCM of 6992 and 7000

1. What is the LCM of 6992 and 7000?

Answer: LCM of 6992 and 7000 is 6118000.

2. What are the Factors of 6992?

Answer: Factors of 6992 are 1, 2, 4, 8, 16, 19, 23, 38, 46, 76, 92, 152, 184, 304, 368, 437, 874, 1748, 3496, 6992. There are 20 integers that are factors of 6992. The greatest factor of 6992 is 6992.

3. What are the Factors of 7000?

Answer: Factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000. There are 32 integers that are factors of 7000. The greatest factor of 7000 is 7000.

4. How to Find the LCM of 6992 and 7000?

Answer:

Least Common Multiple of 6992 and 7000 = 6118000

Step 1: Find the prime factorization of 6992

6992 = 2 x 2 x 2 x 2 x 19 x 23

Step 2: Find the prime factorization of 7000

7000 = 2 x 2 x 2 x 5 x 5 x 5 x 7

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 6118000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 7 x 19 x 23

Step 4: Therefore, the least common multiple of 6992 and 7000 is 6118000.