Least Common Multiple of 7984 and 7986

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7984 and 7986 the smallest integer that is 31880112 that is divisible by both numbers.

Least Common Multiple (LCM) of 7984 and 7986 is 31880112.

LCM(7984,7986) = 31880112

LCM of 7984 and 7986

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

LCM of:
and

Least Common Multiple of 7984 and 7986

LCM of 7984 and 7986 is 31880112

Least common multiple can be found by multiplying the highest exponent prime factors of 7984 and 7986. First we will calculate the prime factors of 7984 and 7986.

Prime Factorization of 7984


2 7984
2 3992
2 1996
2 998
499 499
1

Prime factors of 7984 are 2,499. Prime factorization of 7984 in exponential form is:

7984 = 24×4991

Prime Factorization of 7986


2 7986
3 3993
11 1331
11 121
11 11
1

Prime factors of 7986 are 2, 3,11. Prime factorization of 7986 in exponential form is:

7986 = 21×31×113

Now multiplying the highest exponent prime factors to calculate the LCM of 7984 and 7986.

LCM(7984,7986) = 24×31×113×4991
LCM(7984,7986) = 31880112

Factors of 7984

List of positive integer factors of 7984 that divides 7984 without a remainder.

1, 2, 4, 8, 16, 499, 998, 1996, 3992, 7984

Factors of 7986

List of positive integer factors of 7986 that divides 7986 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726, 1331, 2662, 3993, 7986

Least Common Multiple of 7984 and 7986 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7984 and 7986, than apply into the LCM equation.

GCF(7984,7986) = 2
LCM(7984,7986) = ( 7984 × 7986) / 2
LCM(7984,7986) = 63760224 / 2
LCM(7984,7986) = 31880112

Properties of LCM 7984 and 7986

(i) The LCM of 7986 and 7984 is associative

LCM of 7984 and 7986 = LCM of 7986 and 7984

Related Least Common Multiples of 7984

Related Least Common Multiples of 7986

Frequently Asked Questions on LCM of 7984 and 7986

1. What is the LCM of 7984 and 7986?

Answer: LCM of 7984 and 7986 is 31880112.

2. What are the Factors of 7984?

Answer: Factors of 7984 are 1, 2, 4, 8, 16, 499, 998, 1996, 3992, 7984. There are 10 integers that are factors of 7984. The greatest factor of 7984 is 7984.

3. What are the Factors of 7986?

Answer: Factors of 7986 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726, 1331, 2662, 3993, 7986. There are 16 integers that are factors of 7986. The greatest factor of 7986 is 7986.

4. How to Find the LCM of 7984 and 7986?

Answer:

Least Common Multiple of 7984 and 7986 = 31880112

Step 1: Find the prime factorization of 7984

7984 = 2 x 2 x 2 x 2 x 499

Step 2: Find the prime factorization of 7986

7986 = 2 x 3 x 11 x 11 x 11

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

LCM = 31880112 = 2 x 2 x 2 x 2 x 3 x 11 x 11 x 11 x 499

Step 4: Therefore, the least common multiple of 7984 and 7986 is 31880112.