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
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
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
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
(i) The LCM of 5985 and 5978 is associative
LCM of 5978 and 5985 = LCM of 5985 and 5978
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.