Least Common Multiple of 5978 and 5984

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 5984 the smallest integer that is 17886176 that is divisible by both numbers.

Least Common Multiple (LCM) of 5978 and 5984 is 17886176.

LCM(5978,5984) = 17886176

LCM of 5978 and 5984

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

LCM of:
and

Least Common Multiple of 5978 and 5984

LCM of 5978 and 5984 is 17886176

Least common multiple can be found by multiplying the highest exponent prime factors of 5978 and 5984. First we will calculate the prime factors of 5978 and 5984.

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 5984


2 5984
2 2992
2 1496
2 748
2 374
11 187
17 17
1

Prime factors of 5984 are 2, 11,17. Prime factorization of 5984 in exponential form is:

5984 = 25×111×171

Now multiplying the highest exponent prime factors to calculate the LCM of 5978 and 5984.

LCM(5978,5984) = 25×72×111×171×611
LCM(5978,5984) = 17886176

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 5984

List of positive integer factors of 5984 that divides 5984 without a remainder.

1, 2, 4, 8, 11, 16, 17, 22, 32, 34, 44, 68, 88, 136, 176, 187, 272, 352, 374, 544, 748, 1496, 2992, 5984

Least Common Multiple of 5978 and 5984 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 5984, than apply into the LCM equation.

GCF(5978,5984) = 2
LCM(5978,5984) = ( 5978 × 5984) / 2
LCM(5978,5984) = 35772352 / 2
LCM(5978,5984) = 17886176

Properties of LCM 5978 and 5984

(i) The LCM of 5984 and 5978 is associative

LCM of 5978 and 5984 = LCM of 5984 and 5978

Related Least Common Multiples of 5978

Related Least Common Multiples of 5984

Frequently Asked Questions on LCM of 5978 and 5984

1. What is the LCM of 5978 and 5984?

Answer: LCM of 5978 and 5984 is 17886176.

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 5984?

Answer: Factors of 5984 are 1, 2, 4, 8, 11, 16, 17, 22, 32, 34, 44, 68, 88, 136, 176, 187, 272, 352, 374, 544, 748, 1496, 2992, 5984. There are 24 integers that are factors of 5984. The greatest factor of 5984 is 5984.

4. How to Find the LCM of 5978 and 5984?

Answer:

Least Common Multiple of 5978 and 5984 = 17886176

Step 1: Find the prime factorization of 5978

5978 = 2 x 7 x 7 x 61

Step 2: Find the prime factorization of 5984

5984 = 2 x 2 x 2 x 2 x 2 x 11 x 17

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

LCM = 17886176 = 2 x 2 x 2 x 2 x 2 x 7 x 7 x 11 x 17 x 61

Step 4: Therefore, the least common multiple of 5978 and 5984 is 17886176.