Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6004 and 6009 the smallest integer that is 36078036 that is divisible by both numbers.
Least Common Multiple (LCM) of 6004 and 6009 is 36078036.
LCM(6004,6009) = 36078036
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 6004 and 6009. First we will calculate the prime factors of 6004 and 6009.
Prime Factorization of 6004
2 | 6004 |
2 | 3002 |
19 | 1501 |
79 | 79 |
1 |
Prime factors of 6004 are 2, 19,79. Prime factorization of 6004 in exponential form is:
6004 = 22×191×791
Prime Factorization of 6009
3 | 6009 |
2003 | 2003 |
1 |
Prime factors of 6009 are 3,2003. Prime factorization of 6009 in exponential form is:
6009 = 31×20031
Now multiplying the highest exponent prime factors to calculate the LCM of 6004 and 6009.
LCM(6004,6009) = 22×31×191×791×20031
LCM(6004,6009) = 36078036
Factors of 6004
List of positive integer factors of 6004 that divides 6004 without a remainder.
1, 2, 4, 19, 38, 76, 79, 158, 316, 1501, 3002, 6004
Factors of 6009
List of positive integer factors of 6009 that divides 6009 without a remainder.
1, 3, 2003, 6009
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6004 and 6009, than apply into the LCM equation.
GCF(6004,6009) = 1
LCM(6004,6009) = ( 6004 × 6009) / 1
LCM(6004,6009) = 36078036 / 1
LCM(6004,6009) = 36078036
(i) The LCM of 6009 and 6004 is associative
LCM of 6004 and 6009 = LCM of 6009 and 6004
1. What is the LCM of 6004 and 6009?
Answer: LCM of 6004 and 6009 is 36078036.
2. What are the Factors of 6004?
Answer: Factors of 6004 are 1, 2, 4, 19, 38, 76, 79, 158, 316, 1501, 3002, 6004. There are 12 integers that are factors of 6004. The greatest factor of 6004 is 6004.
3. What are the Factors of 6009?
Answer: Factors of 6009 are 1, 3, 2003, 6009. There are 4 integers that are factors of 6009. The greatest factor of 6009 is 6009.
4. How to Find the LCM of 6004 and 6009?
Answer:
Least Common Multiple of 6004 and 6009 = 36078036
Step 1: Find the prime factorization of 6004
6004 = 2 x 2 x 19 x 79
Step 2: Find the prime factorization of 6009
6009 = 3 x 2003
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 36078036 = 2 x 2 x 3 x 19 x 79 x 2003
Step 4: Therefore, the least common multiple of 6004 and 6009 is 36078036.