Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5998 and 6006 the smallest integer that is 18011994 that is divisible by both numbers.
Least Common Multiple (LCM) of 5998 and 6006 is 18011994.
LCM(5998,6006) = 18011994
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 5998 and 6006. First we will calculate the prime factors of 5998 and 6006.
Prime Factorization of 5998
2 | 5998 |
2999 | 2999 |
1 |
Prime factors of 5998 are 2,2999. Prime factorization of 5998 in exponential form is:
5998 = 21×29991
Prime Factorization of 6006
2 | 6006 |
3 | 3003 |
7 | 1001 |
11 | 143 |
13 | 13 |
1 |
Prime factors of 6006 are 2, 3, 7, 11,13. Prime factorization of 6006 in exponential form is:
6006 = 21×31×71×111×131
Now multiplying the highest exponent prime factors to calculate the LCM of 5998 and 6006.
LCM(5998,6006) = 21×31×71×111×131×29991
LCM(5998,6006) = 18011994
Factors of 5998
List of positive integer factors of 5998 that divides 5998 without a remainder.
1, 2, 2999, 5998
Factors of 6006
List of positive integer factors of 6006 that divides 6006 without a remainder.
1, 2, 3, 6, 7, 11, 13, 14, 21, 22, 26, 33, 39, 42, 66, 77, 78, 91, 143, 154, 182, 231, 273, 286, 429, 462, 546, 858, 1001, 2002, 3003, 6006
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5998 and 6006, than apply into the LCM equation.
GCF(5998,6006) = 2
LCM(5998,6006) = ( 5998 × 6006) / 2
LCM(5998,6006) = 36023988 / 2
LCM(5998,6006) = 18011994
(i) The LCM of 6006 and 5998 is associative
LCM of 5998 and 6006 = LCM of 6006 and 5998
1. What is the LCM of 5998 and 6006?
Answer: LCM of 5998 and 6006 is 18011994.
2. What are the Factors of 5998?
Answer: Factors of 5998 are 1, 2, 2999, 5998. There are 4 integers that are factors of 5998. The greatest factor of 5998 is 5998.
3. What are the Factors of 6006?
Answer: Factors of 6006 are 1, 2, 3, 6, 7, 11, 13, 14, 21, 22, 26, 33, 39, 42, 66, 77, 78, 91, 143, 154, 182, 231, 273, 286, 429, 462, 546, 858, 1001, 2002, 3003, 6006. There are 32 integers that are factors of 6006. The greatest factor of 6006 is 6006.
4. How to Find the LCM of 5998 and 6006?
Answer:
Least Common Multiple of 5998 and 6006 = 18011994
Step 1: Find the prime factorization of 5998
5998 = 2 x 2999
Step 2: Find the prime factorization of 6006
6006 = 2 x 3 x 7 x 11 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 18011994 = 2 x 3 x 7 x 11 x 13 x 2999
Step 4: Therefore, the least common multiple of 5998 and 6006 is 18011994.