Least Common Multiple of 5978 and 5985

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5978 and 5985 the smallest integer that is 5111190 that is divisible by both numbers.

Least Common Multiple (LCM) of 5978 and 5985 is 5111190.

LCM(5978,5985) = 5111190

LCM of 5978 and 5985

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

LCM of:
and

Least Common Multiple of 5978 and 5985

LCM of 5978 and 5985 is 5111190

Least common multiple can be found by multiplying the highest exponent prime factors of 5978 and 5985. First we will calculate the prime factors of 5978 and 5985.

Prime Factorization of 5978


2 5978
7 2989
7 427
61 61
1

Prime factors of 5978 are 2, 7,61. Prime factorization of 5978 in exponential form is:

5978 = 21×72×611

Prime Factorization of 5985


3 5985
3 1995
5 665
7 133
19 19
1

Prime factors of 5985 are 3, 5, 7,19. Prime factorization of 5985 in exponential form is:

5985 = 32×51×71×191

Now multiplying the highest exponent prime factors to calculate the LCM of 5978 and 5985.

LCM(5978,5985) = 21×32×51×72×191×611
LCM(5978,5985) = 5111190

Factors of 5978

List of positive integer factors of 5978 that divides 5978 without a remainder.

1, 2, 7, 14, 49, 61, 98, 122, 427, 854, 2989, 5978

Factors of 5985

List of positive integer factors of 5985 that divides 5985 without a remainder.

1, 3, 5, 7, 9, 15, 19, 21, 35, 45, 57, 63, 95, 105, 133, 171, 285, 315, 399, 665, 855, 1197, 1995, 5985

Least Common Multiple of 5978 and 5985 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5978 and 5985, than apply into the LCM equation.

GCF(5978,5985) = 7
LCM(5978,5985) = ( 5978 × 5985) / 7
LCM(5978,5985) = 35778330 / 7
LCM(5978,5985) = 5111190

Properties of LCM 5978 and 5985

(i) The LCM of 5985 and 5978 is associative

LCM of 5978 and 5985 = LCM of 5985 and 5978

Related Least Common Multiples of 5978

Related Least Common Multiples of 5985

Frequently Asked Questions on LCM of 5978 and 5985

1. What is the LCM of 5978 and 5985?

Answer: LCM of 5978 and 5985 is 5111190.

2. What are the Factors of 5978?

Answer: Factors of 5978 are 1, 2, 7, 14, 49, 61, 98, 122, 427, 854, 2989, 5978. There are 12 integers that are factors of 5978. The greatest factor of 5978 is 5978.

3. What are the Factors of 5985?

Answer: Factors of 5985 are 1, 3, 5, 7, 9, 15, 19, 21, 35, 45, 57, 63, 95, 105, 133, 171, 285, 315, 399, 665, 855, 1197, 1995, 5985. There are 24 integers that are factors of 5985. The greatest factor of 5985 is 5985.

4. How to Find the LCM of 5978 and 5985?

Answer:

Least Common Multiple of 5978 and 5985 = 5111190

Step 1: Find the prime factorization of 5978

5978 = 2 x 7 x 7 x 61

Step 2: Find the prime factorization of 5985

5985 = 3 x 3 x 5 x 7 x 19

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

LCM = 5111190 = 2 x 3 x 3 x 5 x 7 x 7 x 19 x 61

Step 4: Therefore, the least common multiple of 5978 and 5985 is 5111190.