Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7006 and 7014 the smallest integer that is 24570042 that is divisible by both numbers.
Least Common Multiple (LCM) of 7006 and 7014 is 24570042.
LCM(7006,7014) = 24570042
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 7006 and 7014. First we will calculate the prime factors of 7006 and 7014.
Prime Factorization of 7006
2 | 7006 |
31 | 3503 |
113 | 113 |
1 |
Prime factors of 7006 are 2, 31,113. Prime factorization of 7006 in exponential form is:
7006 = 21×311×1131
Prime Factorization of 7014
2 | 7014 |
3 | 3507 |
7 | 1169 |
167 | 167 |
1 |
Prime factors of 7014 are 2, 3, 7,167. Prime factorization of 7014 in exponential form is:
7014 = 21×31×71×1671
Now multiplying the highest exponent prime factors to calculate the LCM of 7006 and 7014.
LCM(7006,7014) = 21×31×71×311×1131×1671
LCM(7006,7014) = 24570042
Factors of 7006
List of positive integer factors of 7006 that divides 7006 without a remainder.
1, 2, 31, 62, 113, 226, 3503, 7006
Factors of 7014
List of positive integer factors of 7014 that divides 7014 without a remainder.
1, 2, 3, 6, 7, 14, 21, 42, 167, 334, 501, 1002, 1169, 2338, 3507, 7014
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7006 and 7014, than apply into the LCM equation.
GCF(7006,7014) = 2
LCM(7006,7014) = ( 7006 × 7014) / 2
LCM(7006,7014) = 49140084 / 2
LCM(7006,7014) = 24570042
(i) The LCM of 7014 and 7006 is associative
LCM of 7006 and 7014 = LCM of 7014 and 7006
1. What is the LCM of 7006 and 7014?
Answer: LCM of 7006 and 7014 is 24570042.
2. What are the Factors of 7006?
Answer: Factors of 7006 are 1, 2, 31, 62, 113, 226, 3503, 7006. There are 8 integers that are factors of 7006. The greatest factor of 7006 is 7006.
3. What are the Factors of 7014?
Answer: Factors of 7014 are 1, 2, 3, 6, 7, 14, 21, 42, 167, 334, 501, 1002, 1169, 2338, 3507, 7014. There are 16 integers that are factors of 7014. The greatest factor of 7014 is 7014.
4. How to Find the LCM of 7006 and 7014?
Answer:
Least Common Multiple of 7006 and 7014 = 24570042
Step 1: Find the prime factorization of 7006
7006 = 2 x 31 x 113
Step 2: Find the prime factorization of 7014
7014 = 2 x 3 x 7 x 167
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 24570042 = 2 x 3 x 7 x 31 x 113 x 167
Step 4: Therefore, the least common multiple of 7006 and 7014 is 24570042.